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1a
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G. Giachetta, M. Mangiarotti, R. Vitolo: The
Einstein-Yang-Mills equations, J. Gen. Rel. Grav.
23, n. 1 (1991), 641-659.
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2a
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R. Vitolo: Spherical symmetry in classical
and quantum Galilei general relativity, Ann. Inst.
`H. Poincaré', 64, n. 2 (1996) 177--203,
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3a
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R. Vitolo: A new infinite order formulation
of variational sequences, Arch. Math. Un.
Brunensis, 34, n. 4 (1998), 483-504; EMS
server.
PDF
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4a
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R. Vitolo: Quantum structures in Galilei
general relativity, Ann. Inst. 'H. Poincaré'
70 n. 3 (1999) 239--258.
PDF
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5a
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R. Vitolo: Finite order variational
bicomplexes, Math. Proc. of the Camb. Phil. Soc.,
125, n. 2 (1999) 321-333; arXiv.org.
PDF
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6a
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R. Vitolo: On different geometric
formulations of Lagrangian formalism, Diff. Geom.
and its Appl., 10, n. 3 (1999), 225--255. Updated version here:
PDF
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7a
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R. Vitolo: Quantum structures in Einstein
general relativity, Lett. Math. Phys. 51
(2000), 119--133,
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8a
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D. Saller, R. Vitolo: Symmetries in covariant
classical mechanics, J. Math. Phys. 41, n.
10, October 2000, 6824-6842, arXiv.org
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9a
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M. Palese, R. Vitolo: On a class of
polynomial Lagrangians, Proc. of the winter school
`Geometry and Physics', Srni (Czech Rep) 2000, Rend.
Mat. Palermo Serie II, Suppl. 66 (2001), 147-159,
arXiv.org
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10a
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M. Francaviglia, M. Palese, R. Vitolo:
Symmetries in finite order variational
sequences, Czech. Math. J. 52 (127) (2002),
197-213.
PDF
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11a
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R. Vitolo: Finite order formulation of
Vinogradov C-spectral sequence, Acta Appl. Math.
70 1-2, (2002) 133-154; arXiv.org
Updated version here:
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12a
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I. Kolár, R. Vitolo: On the Helmholtz
operator for Euler morphism, Math. Proc. of the
Camb. Phil. Soc. 135 (2003), 277-290.
PDF
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13a
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G. Saccomandi, R. Vitolo: Null Lagrangians
for nematic elastomers, Fundamental'naya
i Prikladnaya Matematika 10 (2004) n.1, 17-28,
issue on ``Geometry of integrable models'', A. V.
Kiselev (ed.) (Russian); English translation
in Journal of Mathematical Sciences 136 n. 6 (2006), 4470-4477.
Updated version here:
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14a
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M. Francaviglia, M. Palese, R. Vitolo: A
geometric formulation of Hessian and Jacobi tensors for
higher order Lagrangians, Differential Geometry and
its Applications 22, n. 1 (2005),
105-120.
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15a
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G. Manno, R. Vitolo: Relativistic mechanics,
contact manifolds and symmetries, Note di
Matematica 23, n. 2, 2004/2005, 157-171.
PDF
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16a
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G. Manno, F. Oliveri, R. Vitolo: On
differential equations determined by the group of point
symmetries, Jour. Math. Anal. Appl. 332 (2007), 767-786.
PDF
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17a
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G. Manno, F. Oliveri, R. Vitolo: Differential equations uniquely
determined by algebras of point symmetries,
Theoret. Math. Phys. 151 n. 3 (2007), 843-850
PDF
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18a
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M. Modugno, R. Vitolo: The geometry of
Newton's law and rigid systems, Archivum Math. Univ. Brunensis
43, n. 2 (2007) 197-229; arXiv.org
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19a
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M. Modugno, C. Tejero Prieto, R. Vitolo: A
covariant approach to the quantisation of a rigid
body, J. Phys. A: Math. theor. 41 (2008) 035304, see arXiv.org.
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20a
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G. Manno, R. Vitolo: Geometric aspects of
higher order variational principles on submanifolds,
Acta Appl. Math. 101 (2008), 215-229.
PDF.
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21a
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G. Manno, J. Pohjanpelto, R. Vitolo:
Symmetries, conservation laws and variational principles for gauge
theories, J. Geom. Phys. 58 (2008), 996-1006.
PDF.
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22a
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P.H.M. Kersten, I.S. Krasil'shchik, A.M. Verbovetsky, R. Vitolo:
Integrability of Kupershmidt's deformation, Acta Appl. Math. 109 no. 1 (2010), 75-86.
arXiv.org
PDF.
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23a
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J. Janyska, M. Modugno, R. Vitolo: An algebraic approach to physical scales
, Acta Appl. Math. 110, no. 3 (2010), 1249-1276.
arXiv.org.
PDF.
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24a
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I. Kolar, R. Vitolo: Absolute contact differentiation on submanifolds of
Cartan spaces
, Differential Geometry and its Applications, Volume 28, Issue 1 (2010), 19--32.
PDF.
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25a
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P. Kersten, I.S. Krasil'shchik, A.M. Verbovetsky, R.
Vitolo: On integrable structures for a generalized Monge-Ampere
equation
, Theor. Math. Phys. 128, no. 2 (2012),
600-615.
arXiv.org.
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26a
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I.S. Krasil'shchik, A.M. Verbovetsky, R.
Vitolo: A unified approach to computation of integrable structures
, Acta Appl. Math. 120, no. 1 (2012), 199-218.
arXiv.org.
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27a
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G. Saccomandi, R.
Vitolo: A Translation of
the T. Levi-Civita paper: Interpretazione Gruppale degli Integrali di
un Sistema Canonico, Rend. Acc. Lincei, s. 3a, vol. VII,
2o sem. 1899, pp. 235--238 , Regular and Chaotic Dynamics
Volume 17, Issue 1, pp. 105-112 (2012).
arXiv.org.
Download here the original paper by Levi-Civita.
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28a
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J. Janyska, R. Vitolo: On the characterization of
infinitesimal symmetries of the relativistic phase space
J. Phys. A: Math. Theor. 45 (2012) 485205 (28pp).
PDF
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29a
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E.V. Ferapontov, M.V. Pavlov, R.F. Vitolo:
Projective-geometric aspects of homogeneous third-order
Hamiltonian operators, J. Geom. Phys. 85
(2014),
16--18
PDF
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30a
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G. Manno, F. Oliveri, G. Saccomandi, R. Vitolo:
Ordinary differential equations described by their Lie symmetry
algebra, J. Geom. Phys. (2014), 85 (2014),
2--15
PDF
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31a
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C. Tejero Prieto, R. Vitolo:
On the geometry of the energy operator in quantum
mechanics,
International Journal of Geometric Methods in Modern Physics,
Vol. 11, No. 07 (2014): 1460027.
PDF
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32a
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G. Saccomandi, R. Vitolo:
On the Mathematical and Geometrical Structure of the
Determining Equations for Shear Waves in Nonlinear Isotropic Incompressible
Elastodynamics, J. Math. Phys. 55 (2014), 081502, PDF
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33a
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M.V. Pavlov, R.F. Vitolo:
On the Bi-Hamiltonian Geometry of WDVV Equations,
Lett. Math. Phys. 105 no. 8 (2015), 1135--1163.
arXiv.org,
PDF
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34a
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E.V. Ferapontov, M.V. Pavlov, R.F. Vitolo:
Towards the classification of homogeneous third-order
Hamiltonian operators ,
Int. Math. Res. Notices 22 (2016), 6829-6855,
arXiv.org,
PDF
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35a
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E. Pucci, G. Saccomandi, R. Vitolo:
Bogus Transformations in Mechanics of Continua, Int. J. of
Eng. Sci. 99 (2016), 13--21,
PDF
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36a
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A. Sergyeyev, R. Vitolo:
Symmetries and conservation laws for the
Karczewska--Rozmej--Rutkowski--Infeld equation, Nonlinear
Analysis: Real World Applications 32 (2016) 1-9.
arxiv.org
PDF
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37a
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M.V. Pavlov, R.F. Vitolo:
Remarks on the Lagrangian representation of bi-Hamiltonian
equations, J. Geom. Phys. 113C (2017),
239-249. DOI:
http://dx.doi.org/10.1016/j.geomphys.2016.10.013.
arxiv.org
PDF
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38a
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P. Lorenzoni, A. Savoldi, R. Vitolo:
Bi-Hamiltonian structures of KdV-type, J. Phys. A:
Math. Theor. 51 no. 4 (2018), 045202.
arxiv.org
PDF
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39a
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C. Tejero Prieto, R. Vitolo:
The geometry of real reducible polarizations in quantum
mechanics, J. Phys. A: Theor. Math. 50
no. 10 (2017), 105205; DOI:
https://doi.org/10.1088/1751-8121/aa58c7
arxiv.org
PDF
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40a
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E.V. Ferapontov, M.V. Pavlov, R.F. Vitolo:
Systems of conservation laws with third-order Hamiltonian
structures, Lett. Math. Phys.
108, Issue 6 (2018), 1525-1550
arxiv.org
PDF
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41a
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M. Casati, E.V. Ferapontov, M.V. Pavlov, R.F. Vitolo:
On a class of third-order nonlocal Hamiltonian operators,
J. Geom. Phys., 138 (2019), 285--296
arxiv.org
DOI,
PDF
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42a
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R. Vitolo:
Computing with Hamiltonian operators,
Computer Physics Communications Volume 244 (2019), 228-245,
arxiv.org
PDF
Reduce programs of computations with Hamiltonian operators
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43a
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S. Carrino, F. Nicassio, G. Scarselli, R. Vitolo:
Finite difference model of wave motion for Structural
Health Monitoring of Single Lap Joints,
Int. J. of Solids and Structures, 161
(2019), 219--227,
DOI
PDF
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44a
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M.V. Pavlov, R.F. Vitolo:
Bi-Hamiltonian structure of the Oriented Associativity equation
,
J. Phys. A: Theor. Math. - Letters, Volume 52, Number 20
DOI (2019),
arxiv.org
PDF,
Reduce programs.
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45a
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M. Casati, P. Lorenzoni, R. Vitolo:
Three computational approaches to weakly nonlocal
Poisson brackets , Studies in Applied Mathematics 144 no. 4
(2020) 412–448, DOI: 10.1111/sapm.12302,
arxiv.org
PDF
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46a
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P. Lorenzoni, R. Vitolo:
Weakly nonlocal Poisson brackets, Schouten brackets and
supermanifolds , J. Geom. Phys. 149 (2020)
103573,
arxiv.org
PDF
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47a
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P. Vergallo, R. Vitolo:
Homogeneous Hamiltonian operators and the theory of
coverings , Diff. Geom and its Appl. 75
(2021) 101713,
arxiv.org
PDF
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48a
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M.V. Pavlov, P. Vergallo, R. Vitolo:
Classification of bi-Hamiltonian pairs extended by
isometries ,
Proceedings
of the Royal Society A 20210185 (2021);
arxiv.org
PDF
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49a
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M. Casati, P. Lorenzoni, D. Valeri, R. Vitolo:
Weakly nonlocal Poisson brackets: tools, examples, computations
, Computer Physics Communications 274 (2022) 108284,
DOI,
arxiv.org
PDF
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50a
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J. Vašíček, R. Vitolo:
WDVV equations and invariant bi-Hamiltonian formalism
Journal
of High Energy Physics 129 (2021),
arxiv.org
PDF
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51a
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S. De Bartolo, S. Rizzello, E. Ferrari, F. Frega, G. Napoli,
R. Vitolo, M. Scaraggi, C. Fallico, G. Severino:
Scaling behaviour of braided active channels: a Taylor's
power law approach
, Eur. Phys. J. Plus (2022) 137:622,
DOI
PDF
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52a
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F. Nicassio, P. Vergallo, R. Vitolo, G. Scarselli:
Two dimensional finite different model with
Singularity Attenuation Factor Evaluation (SAFE) for structural health
monitoring of single lap joints
, Structural Control and Health Monitoring, vol. 2023,
Article ID 1429761, 13 pages (2023).
DOI.
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53a
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J. Vašíček, R. Vitolo::
WDVV equations: symbolic computations of Hamiltonian operators
, Applicable Algebra in Engineering, Communication and
Computing
DOI,
arxiv.org
PDF
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54a
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P. Vergallo, R. Vitolo:
Projective geometry of homogeneous second order Hamiltonian
operators
, Nonlinearity 36 (2023) 5311--5333,
DOI
(open access)
arXiv.
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55a
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P. Lorenzoni, S. Shadrin, R. Vitolo:
Miura-reciprocal transformations and localizable Poisson pencils,
Nonlinearity 37 (2024), 025001 (35pp),
DOI,
arXiv.org
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56a
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S. Rizzello, G, Napoli, R. Vitolo, S. De Bartolo:
Master equation model for solute transport in river basins: part I
channel fluvial scale, Stochastic Environmental Research and Risk
Assessment 37, 3807--3817 (2023),
DOI.
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57a
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P. Angeletti, G. Toso, R. Vitolo:
Asymptotic
Phase Synthesis by Transport Maps - Part I: Theory and Irrotational Linear
Maps, submitted for publication (2023).
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58a
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P. Angeletti, G. Toso, R. Vitolo:
Asymptotic
Phase Synthesis by Transport Maps - Part II: Optimal Transport Problem,
submitted for publication (2023).
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59a
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S. Rizzello, G, Napoli, R. Vitolo, S. De Bartolo:
Master equation model for solute transport in river basins: part II
basin fluvial scale,
Stochastic Environmental Research and Risk
Assessment 38, 751–760 (2024),
DOI.
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60a
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P. Lorenzoni, R. Vitolo:
Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge
metrics, preprint (2023),
arXiv,
Reduce
programs.
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61a
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S. Rizzello, M. Scaraggi, A.D. Nelson, L. Primavera,
G. Napoli, G. Stecca, R. Vitolo, S. De Bartolo:
Multiscaling
behavior of braided channel networks: An alternative formulation of
Taylor's law variate transformations,
Phys. Rev. E 109, 034306 (2024),
DOI.
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62a
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S. Opanasenko, R. Vitolo:
Bi-Hamiltonian structures of WDVV-type,
to appear in Proc. Royal Society A (2024),
arXiv.
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1c
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R. Vitolo: Some aspects of first-order
variational sequences in mechanics, Proc. of the VI
Conf. in Diff. Geom. and its Appl., Brno 1995, 487--494; EMS
server
PDF
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2c
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M. Modugno, R. Vitolo: Quantum Connection and
Poincar\'e-Cartan form, Proc. of the conference in
honour of A. Lichnerowicz, Frascati, october 1995; ed.
G. Ferrarese, Pitagora, Bologna 1996, 237-279;
PDF
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3c
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R. Vitolo: Quantum structures in general
relativistic theories, Proc. of the XII National.
Conf. of Gen. Rel. and Grav. Phys., Roma (1996), World
Scientific, 375-359;
PDF
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4c
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M. Francaviglia, M. Palese, R. Vitolo:
Superpotentials in variational sequences, Proc.
of the VII Conf. on Diff. Geom and Appl., Brno 1998, 469-480;
EMS
server.
PDF
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5c
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R. Vitolo: Quantising the rigid body,
Proc. of the VII Conf. on Diff. Geom and Appl., Brno
1998, 653-664; EMS
server.
PDF
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6c
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M. Modugno, C. Tejero Prieto, R. Vitolo:
Comparison between Geoometric Quantisation and
Covariant Quantum Mechanics, Proceedings of Lie
Theory and Its Applications in Physics III (World
Scientific, 2000), edited by H.-D. Doebner, V.K. Dobrev
and J. Hilgert, 155-175; arXiv.org
PDF
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7c
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G. Manno, R. Vitolo: Variational sequences on
finite order jets of submanifolds, Proc. of the
VIII int. conf. on Diff. Geom. and its Appl., Opava
(Czech Rep.), 2001, 435-446;
PDF
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8c
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S. Igonin, A. Verbovetsky, R. Vitolo:
Variational Multivectors and Brackets in the
Geometry of Jet Spaces, V Int. Conf. on on Symmetry
in Nonlinear Mathematical Physics, Kyiv 2003 Inst. of
Mathematics, Nat. Acad. of Sciences of Ukraine, 1335-1342;
PDF
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9c
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F. Oliveri, G. Manno, R. Vitolo:
On an Inverse Problem in Group Analysis of PDE's:
Lie--Remarkable Equations,
Proceedings XIII International Conference on Waves and
Stability in Continuous Media, World Scientific Co., Singapore, 2006, 420-431;
PDF
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10c
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F. Oliveri, G. Manno, R. Vitolo:
Lie--Remarkable PDEs,
in "Asymptotic methods in nonlinear wave phenomena",
in honour of the 65th birthday of Antonio Greco,
World Scientific Co., Singapore, 2007, 119-131;
PDF
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11c
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F. Oliveri, G. Manno, R. Vitolo:
On the correspondence between differential equations and
symmetry algebras, Symmetry and Perturbation Theory,
proceedings of the conference in Otranto, 2/6--9/6/2007, World
Scientific 2007, 164-171. PDF
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12c
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R. Vitolo:
Finite order variational sequences: a short review,
Proceedings of the conference in honour of D. Krupka,
O. Krupková, D. Saunders eds., Nova Science Publisher 2008
(Olomouc, Czech Rep.), 117--136.
PDF
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13c
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P.H.M. Kersten, I.S. Krasil shchik, A.M. Verbovetsky, R. Vitolo:
Hamiltonian structures for general PDEs, in B. Kruglikov, V. Lychagin, E.
Straume: Differential Equations -- Geometry, Symmetries and Integrability,
Proceedings of the 2008 Abel Symposium, Springer, 187-198.
PDF
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14c
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M. Modugno, C. Tejero Prieto, R. Vitolo:
Geometric aspects of the quantization of a rigid body,
in B. Kruglikov, V. Lychagin, E.
Straume: Differential Equations -- Geometry, Symmetries and Integrability,
Proceedings of the 2008 Abel Symposium, Springer, 275-285.
PDF
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15c
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F. Oliveri, G. Manno, R. Vitolo:
Differential equations and Lie symmetries,
Proceedings XIV International Conference on Waves and
Stability in Continuous Media, N. Manganaro, R. Monaco, S. Rionero
eds., World Scientific Co., Singapore, 2008, 459-468;
PDF
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16c
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G. Scarselli, F. Nicassio, P. Vergallo, R. Vitolo:
Finite difference 3D model for structural health monitoring of
single lap joints,
Proceedings Volume 12047, Nondestructive Characterization and
Monitoring of Advanced Materials, Aerospace, Civil Infrastructure, and
Transportation XVI; 120470E (2022), Event: SPIE Smart Structures +
Nondestructive Evaluation, 2022, Long Beach, California, United
States, DOI.
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17c
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P. Lorenzoni, R. Vitolo:
Projective-geometric
aspects of bi-Hamiltonian structures of KdV type,Contemporary
Mathematics, Volume 788, 2023, American Mathematical Society,
DOI.
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