Geometry, Symmetry and Dynamics


Group members:


Former members:
Collaborators:

We aim at studying the interplay between Geometry, Symmetry, and Dynamics;
with a special view at solution methods for nonlinear differential equations.

In particular, we study

The group meets regularly at irregular dates.

Two meetings on "Geometry and Symmetry of Differential Equations" (GSDE)
were organized in Santa Marinella near Rome in 2006 and in 2010.
See also the conferences "Symmetry and Perturbation Theory" (SPT)

Papers by G. Gaeta

Papers by G. Cicogna

Papers by P. Morando

Papers by D. Catalano Ferraioli
 


Recent publications and preprints



2015

M. Cadoni and G. Gaeta,
``Speed selection for coupled wave equations'',
J. Nonlin. Math. Phys. 22 (2015), 275-297

G. Cicogna, G. Gaeta and S. Walcher,
``Side conditions for ordinary differential equations'',
J. Lie Theory 25 (2015) 125-146

G. Cicogna and F. Pegoraro,
``Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach'',
Phys. Plasmas 22 (2015), 022520

G. Gaeta,
``Symmetry and Lie-Frobenius reduction of differential equations'',
J.Phys. A 48 (2015),  015202

G. Gaeta,
``Poincare'-like approach to Landau theory. I: General theory'',
J. Math. Phys. 56 (2015), 083504

G. Gaeta,
``Poincare'-like approach to Landau theory. II. Simplyfying the
Landau-deGennes potential for nematic liquid crystals'',
J. Math. Phys. 56 (2015), 083505

G. Gaeta and M.A. Rodriguez,
``Symmetry and quaternionic integrable systems'',
J. Geom. Phys. 87 (2015), 134-148

P. Morando,
``Reduction by lambda-symmetries and sigma-symmetries: a Frobenius approach''
J. Nonlin. Math. Phys. 22 (2015), 47-59

2014

D. Catalano Ferraioli and P. Morando,
``Integration of some examples of geodesic flows via solvable structures'',
J. Nonlin. Math. Phys. 21 (2014), 521-532

G. Cicogna,
``Generalized notions of symmetry of ODEs and reduction procedures'',
Mathematical Methods in the Applied Sciences 37 (2014), 1819-1827

G. Gaeta and M.A. Rodriguez,
``Canonical transformations for hyperkahler structures and hyperhamiltonian dynamics'',
J. Math. Phys. 55 (2014), 052901 (26pp)

G. Gaeta, ``Simple and collective twisted symmetries'',
 J. Nonlin. Math. Phys. 21 (2014), 593-627


2013


G. Cicogna,
``On the connections between symmetries and conservation rules of dynamical systems'',
Mathematical Methods in the Applied Sciences 36 (2013), 208-215

G. Cicogna, G. Gaeta and S. Walcher,
``Orbital reducibility and a generalization of $\lambda$-symmetries'',
J. Lie Theory 23 (2013), 357-381

G. Cicogna, G. Gaeta and S. Walcher,
``Dynamical systems and sigma-symmetries'',
J. Phys. A 46 (2013), 235204 (23pp)

2012
D. Catalano Ferraioli and A. M. Vinogradov,
``Differential invariants of generic parabolic Monge–Ampère equations'',
Journal of Physics A 45 (2012): 265204

G. Cicogna,
``Addendum to: Symmetry classification of quasi-linear PDE’s. II: an exceptional case'',
Nonlinear Dynamics 67 (2012), 2909-2912

G. Cicogna,
``Symmetry properties and reduction procedures for ODE's'',
in: Numerical Analysis and Applied Mathematics ICNAAM 2012 vol. 1479 AIP publishing 2012

G. Cicogna,
``Normal Forms of Dynamical Systems'',
in:  Bifurcation, Symmetry and Patterns (ed. by J. Buescu et al., Springer 2012), 129-134

G. Cicogna, G. Gaeta, and S. Walcher,
``A generalization of lambda-symmetry reduction for systems of ODEs: sigma-symmetries''
J. Phys. A 45 (2012), 355205 (29 pp)

G. Gaeta and M.A. Rodriguez,
``Hyperkahler structure of the Taub-NUT metric'',
J. Nonlin. Math. Phys. 19 (2012), 1250014 (10 pages)

P. Morando and S. Sammarco,
``Variational problems with symmetry: a Pfaffian systems approach'',
Acta Appl. Math. 120 (2012), 255-274

P. Morando and S. Sammarco,
``Reduction of exterior differential systems for ordinary variational problems'',
J. Phys. A 45 (2012), 065202 (18 pp)


2011


G. Cicogna,
``Addendum to: Symmetry classification of quasi-linear PDE’s. II: an exceptional case'',
Nonlinear Dynamics (2011)

G. Cicogna
``Symmetries and Constants of Motion of Dynamical Systems'',
ICNAAM 2011.
AIP Conference Proceedings, Volume 1389, pp. 1376-1377 (2011)

G. Cicogna,
``Lambda-symmetries of dynamical systems, Hamiltonian and Lagrangian equations'',
in Proceedings of Workshop on Group Analysis of Differential Equations and Integrable Systems, Protaras, Cyprus

G. Gaeta:
``Gauge fixing and twisted prolongations'',
J. Phys. A: Math. Theor. 44 (2011), 325203 (9 pp)

G. Gaeta:
``Quaternionic integrability'',
J. Nonlin. Math. Phys. 18 (2011), 461-474


2010

 
G. Cicogna,
``Lambda-symmetries of Dynamical Systems, Hamiltonian and Lagrangian equations'',
Proceedings of Workshop on Group Analysis of Differential Equations and Integrable Systems, Protaras, Cyprus, June 2010

G. Cicogna, F. Pegoraro, and F. Ceccherini
``Symmetries, weak symmetries, and related solutions of the Grad–Shafranov equation''
Phys. Plasmas 17, 102506 (2010) (8 pages)

G. Cicogna,
``Symmetries and (Related) Recursion Operators of Linear Evolution Equations''
Symmetry  2 (2010), 98-111

2009

D. Catalano Ferraioli and P. Morando
``Local and nonlocal solvable structures in ODEs reduction''
J. Phys. A: Math. Theor. 42 (2009) 035210 (15pp)

D. Catalano Ferraioli and P. Morando
``Application of solvable structures to the nonlocal symmetry reduction of ODEs''
J. Nonlin. Math. Phys. 16 (2009), S1.27-S1.42

G. Cicogna
"Symmetries of Hamiltonian equations and Lambda-constants of motion"
J. Nonlin. Math. Phys. 16 (2009), S1.43-S1.60

G. Gaeta:
``A gauge-theoretic description of mu-prolongations,
and mu-symmetries of differential equations''
J. Geom. Phys. 59 (2009), 519-539

G. Gaeta
``Twisted symmetries of differential equations''
J. Nonlin. Math. Phys. 16 (2009), S1.107-S1.136

G. Gaeta and G. Cicogna
``Twisted symmetries and integrable systems''
Int. J. Geom. Meths. Mod. Phys. 6 (2009), 1305-1321
 

2008

G. Cicogna,
``Reduction of systems of first-order differential equations via Lambda-symmetries''
Physics Letters A 372 (2008), 3672-3677

G. Cicogna:
``Symmetry classification of quasi-linear PDE's containing arbitrary functions'',
Nonlinear Dynamics 51 (2008), 309-316

G. Gaeta:
``Breaking of linear symmetries and Michel theory:
Grassmann manifolds, and invariant subspaces'';
Int. J. Mod. Phys. A 23 (2008), 547-565

G. Gaeta, F.D. Grosshans, J. Scheurle, S. Walcher:
``Reduction and reconstruction for symmetric ordinary differential equations''
J. Diff. Eqs. 244 (2008), 1810-1839

G. Gaeta and M.A. Rodriguez:
``On the physical applications of hyperhamiltonian dynamics''
J. Phys. A: Math. Theor. 41 (2008) 175203

E. Tassi, F. Pegoraro and G. Cicogna:
``Solutions and symmetries of force-free magnetic fields''
Phys. Plasmas 15 (2008), 092113

2007

M. Cadoni, R. De Leo and G. Gaeta:
``Sine-Gordon solitons, auxiliary fields, and singular limit of a double pendulums chain'',
J. Phys. A: Math. Theor. 40 (2007), 12917-12929

M. Cadoni, R. De Leo and G. Gaeta:
``A symmetry breaking mechanism for selecting the speed of relativistic solitons'',
J. Phys. A: Math. Theor. 40 (2007), 8517-8534

D. Catalano Ferraioli:
``Nonlocal aspects of lambda-symmetries and ODEs reduction'',
J. Phys. A: Math. Theor. 40 (2007), 5479-5489

D. Catalano Ferraioli, G. Manno and F. Pugliese:
``Generalized symmetries of partial differential equations via complex transformations'',
Bull. Austral. Math. Soc. 76 (2007), 243-262

D. Catalano Ferraioli and P. Morando:
``Symmetries and first integrals for non-variational equations'',
Int. J. Geom. Meths. Mod. Phys.  4 (2007), 1217-1230

G. Cicogna and G. Gaeta:
``Noether theorem for mu-symmetries'',
J. Phys. A: Math. Theor. 40 (2007), 11899-11921

G. Gaeta:
``Smooth changes of frame and prolongations of vector fields'',
Int. J. Geom. Meths. Mod. Phys. 4 (2007), 807-827

P. Morando:
``Deformation of Lie derivative and mu-symmetries'',
J. Phys. A: Math. Theor. 40 (2007), 11547--11559
 

2006

D. Catalano Ferraioli and A. M. Vinogradov
``Ricci flat 4-metrics with bidimensional null orbits.
Part I. General aspects and nonabelian case'';
Acta Applicandae Mathematicae 92 (2006), 209-225

D. Catalano Ferraioli and A. M. Vinogradov
``Ricci flat 4-metrics with bidimensional null orbits.
Part II. The Abelian case'';
Acta Applicandae Mathematicae 92 (2006), 226-239

G. Cicogna, F. Ceccherini and F. Pegoraro:
``Applications of symmetry methods to the theory of plasma physics'',
SIGMA (Symm. Integr. Geom. Meths. Appl.) 2 (2006), Paper 017 (17 pages)

G. Cicogna and M. Laino:
''On the notion of conditional symmetry of differential equations'',
Rev. Math. Phys.18 (2006), 1-18

G. Gaeta:
''The Poincaré-Lyapounov-Nekhoroshev theorem for involutory systems of vector fields'',
Ann. Phys. (N.Y.) 321 (2006), 1277-1295

G. Gaeta:
Finite group symmetry breaking"
in: Encyclopedia of Mathematical Physics
(J.P. Francoise, G. Naber & S.T. Tsou editors)
Academic Press, 2006
(preprint version at arXiv:math-ph/0510010)

G. Gaeta and S. Walcher:
``Embedding and splitting ordinary differential equations in normal form'';
J. Diff. Eqs. 224 (2006), 98-119
 

2005

D. Catalano Ferraioli, G. Manno and F. Pugliese:
``Contact symmetries of the elliptic Euler-Darboux equation'',
Note di Matematica 23 (2005), 3-14

F. Ceccherini, G. Cicogna and F. Pegoraro:
``Symmetry properties of some Euler-type equations in plasma physics'',
J. Phys. A: Math. Gen.  38 (2005) 4597-4610

F. Ceccherini, C. Montagna, F. Pegoraro and G. Cicogna:
``Two-dimensional Harris-Liouville plasma kinetic equilibria'',
Phys. Plasmas 12 (2005), 052506

G. Cicogna
``Symmetries and symmetry-invariant solutions of differential equations''
Note di Matematica 23 (2005), no. 2, 15-31

G. Gaeta:
``Asymptotic symmetries in an optical lattice'',
Phys. Rev. A 72 (2005), 033419

G. Gaeta, D. Levi and R. Mancinelli:
``Asymptotic symmetries of difference equations on a lattice'',
J. Nonlin. Math. Phys. 12 (2005), S2.137-S2.146

G. Gaeta and R. Mancinelli:
``Asymptotic scaling symmetries for nonlinear PDEs'',
Int. J. Geom. Meths. Mod. Phys. 2 (2005), 1081-1114

G. Gaeta and R. Mancinelli:
``Asymptotic symmetries of anomalous reaction-diffusion equations'',
J. Nonlin. Math. Phys. 12 (2005), 550-566

G. Gaeta and P. Morando:
``PDEs reduction and lambda-symmetries'';
Note di Matematica 23 (2005), 33-73

G. Gaeta, P. Morando and T. Turgut:
``Symmetry reduction in the variational approach to Liouville dynamics'',
Int. J. Geom. Meths. Mod. Phys. 2 (2005), 657-674

G. Gaeta and S. Walcher:
``Dimension increase and splitting for Poincaré-Dulac normal forms'';
J. Nonlin. Math. Phys. 12 (2005), S1.327-S1.342

2004

G. Cicogna:
``Weak symmetries and adapted variables for differential equations'',
Int. J. Geom. Meth. Mod. Phys.  1 (2004), 23--31

G. Cicogna,
``A discussion on the different notions of symmetry of differential equations'',
Proc. Nat. Acad. Sci. Ukraine  50 (2004), 77-84

G. Cicogna, G. Gaeta and P. Morando:
``On the relation between standard and mu-symmetries for PDEs'';
J. Phys. A: Math. Gen.  37 (2004), 9467-9486

G. Gaeta:
``Lie-Poincaré transformations and a reduction criterion in Landau theory'';
 Ann. Phys. (N.Y.) 312 (2004), 511-540

G. Gaeta:
``Symmetry of stochastic equations'';
Proc. Nat. Acad. Sci. Ukraine  50 (2004), 98-109

G. Gaeta and P. Morando:
``Variational principles for involutive systems of vector fields'';
Int. J. Geom. Meth. Mod. Phys. 1 (2004), 201-232

G. Gaeta and P. Morando:
``Maximal degree variational principles and Liouville dynamics'';
Diff. Geom. Appl.  21 (2004), 27-40

G. Gaeta and P. Morando:
``On the geometry of lambda-symmetries, and PDEs reduction'';
J. Phys. A: Math. Gen.  37 (2004), 6955-6975

2003

G. Gaeta:
``The Poincaré-Nekhoroshev map'';
J. Nonlin. Math. Phys. 10 (2003), 51-64

G. Gaeta and P. Morando:
``A variational principle for volume-preserving dynamics'';
J. Nonlin. Math. Phys. 10 (2003), 539-554

P. Morando and M. Tarallo:
``Hyper-Hamiltonian dynamics and quaternionic regularity'';
Modern Phys. Lett. A 18 (2003), 1841-1847

Other groups and peoples working on similar (or however related) themes

Ian Anderson
José F. Carinena
Giampaolo Cicogna
Mark Fels
Alberto Ibort
Niky Kamran
Decio Levi
Giuseppe Marmo
Concepcion Muriel
Peter Olver
Olga Rossi
Jan Sanders
Alexander Vinogradov
Raffaele Vitolo
Sebastian Walcher
Pavel Winternitz

Symmetry links (maintained in Kiev)
SPT conferences

G.Gaeta, 16/10/2015