Stability in Hamiltonian dynamics and beyond (n. 2022FPZEES)
Type
PRIN 2022, D.D. n. 104 del 2 febbraio 2022
CUP
C53D23002480006
Principal Investigator
Alfonso Sorrentino (Università degli Studi di ROMA "Tor Vergata")
Other research units
UO1 - Alfonso SORRENTINO - Università degli Studi di ROMA "Tor Vergata"
UO2 - Luigi CHIERCHIA - Università degli Studi ROMA
UO3 - Vivina Laura BARUTELLO - Università degli Studi TORINO
UO4 - Francesco FASSO' - Università degli Studi di PADOVA
Duration
28/09/2023 - 28/02/2026
Description
The core of the PRIN Project is concerned with some of the most important theoretical aspects in the study of Hamiltonian systems and their stability properties, as well as with the urgent and timely quest for extending this analysis and the available tools beyond the current range of applicability.
In particular, we focus on four cutting-edge lines of research:
Transition from integrability.
Billiards as prototypical models.
Singular Hamiltonian systems.
Beyond the Hamiltonian realm.
The connection among these problems is twofold. On the one hand, they are all motivated by the quest for a better understanding of the dynamical and stability properties of Hamiltonian systems (and beyond), a subject that has a long-established tradition and has been recently boosted by important breakthroughs, including some by members of the team. On the other hand, the methods that we plan to apply provide natural links among them.
This PRIN Project consolidate a network of 4 internationally recognized Italian research groups in Hamiltonian dynamics, dynamical systems, and geometric mechanics, each contributing with their different and complementary expertise. Due to the interdisciplinary nature, in fact, advances in these subjects require the synergy among different points of view and the combination of diverse techniques, conditions that are hardly available at the level of a single research unit.
Activities
Conferenze:
1) "Stability in Hamiltonian Dynamics and Beyond" (Roma, 1 e 2 Febbraio 2024)
2) "Stability in Hamiltonian dynamics and beyond II" (Torino, January 9-10 2025)
https://sites.google.com/view/stability-ham-dyn-2/home-page
3) "Stability of Hamiltonian Systems and Beyond" + "Fasso`Fest" (Padova, January 26-29+30-31 2026)
https://sites.google.com/view/stability-hamiltonian-beyond/home
https://sites.google.com/view/fasso-day/home
Postdoc:
Sono state create tre posizioni di postdoc: una di 18 mesi all'Universita` di Padova, una di 12 mesi a Roma Tor Vergata e una di 24 mesi a Torino.
Related publications
Bessi U. Counting periodic orbits on fractals weighted by their Lyapunov exponents. Proceedings of the Edimburgh Mathematical Society, 66, 710-757, (2023).
Bessi U. Harmonic embeddings of the stretched Sierpinski gasket. NoDEA, 30, (2023).
Siconolfi A.; Sorrentino A. Aubry-Mather theory on graphs. Nonlinearity 36 (11): 5819, (2023).
Barutello V.; De Blasi I.; Terracini S. Chaotic dynamics in refraction galactic billiards. Nonlinearity, Volume 36, Number 8, (2023).
Biasco L.; Chierchia L. Global properties of generic real–analytic nearly–integrable Hamiltonian systems. Journal of Differential Equations 385, 325–361, (2024).
Baracco L.; Bernardi O.; Lange C.; Mazzucchelli M. On the local maximizers of higher capacity ratios. To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2024).
Baracco L.; Bernardi O. Totally integrable symplectic billiards are ellipses. Advances in Mathematics, Volume 454, (2024).
Bernardi O.; Florio A.; Leguil M. Birkhoff attractors of dissipative billiards. To appear in Ergodic Theory and Dynamical Systems (ETDS).
Argentieri F.; Chierchia L. Isolated Diophantine numbers. To appear in Regular and Chaotic Dynamics, (2024).
Chierchia L.; Fascitiello I. Nineteen Fifty-four: Kolmogorov’s new 'metrical approach' to Hamiltonian Dynamics. To appear in Regular and Chaotic Dynamics, (2024).
Baracco L.; Bernardi O.; Nardi, A. Higher order terms of Mather's β-function for symplectic and outer billiards. Journal of Mathematical Analysis and Applications, Volume 537, Issue 2, 15 (2024).
García-Naranjo L.C.; Marrero J.C.; Martín de Diego D.; Petit Valdés E.P. Almost-Poisson brackets for nonholonomic systems with gyroscopic terms and Hamiltonisation. J. Nonlinear Sci. 34 110 (2024).
García-Naranjo L.C.; Ortega R.; Ureña A.J. Invariant measures as obstructions to attractors in dynamical systems and their role in nonholonomic mechanics. Reg. and Chaot. Dyn. 29 (2024) 751-763.
Baracco L.; Bernardi O.; Nardi, A. Bialy-Mironov type rigidity for centrally symmetric symplectic billiards. (2024) To appear in Nonlinearity.
Baranzini S.; Canneori G.M. Chaotic Phenomena for Generalised N-centre Problems. Arch Rational Mech Anal 248, 39 (2024).
Baranzini S.; Canneori G.M.; Terracini S. Mountain pass frozen planet orbits in the helium atom model. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024) published online first.
Booß-Bavnbek B.; Ji, Y.; Portaluri A.; Zhu C. The dichotomy of forms and operators and the role of Green's forms. Springer, Cham, 2023, 53–70.
Baranzini S.; Portaluri A.; Yang R. Morse index of circular solutions for attractive central force problems on surfaces. J. Math. Anal. Appl. 537 (2024), no. 1, Paper No. 128250, 33 pp.
Constantineau K.; García-Azpeitia C.; García-Naranjo L. C.; Lessard J. P. Determination of stable branches of relative equilibria of the N-vortex problem on the sphere. Commun. Math. Phys. Volume 406, article number 47 (2025).
Costa-Villegas M.; Garcíıa-Naranjo L. C. Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane. Reg. and Chaot. Dyn. 30 (2025) 354-381.
Fassò F.; Sansonetto N. Symplectization of certain Hamiltonian systems in fibered almost symplectic manifolds. Geometric Mechanics 2 (2025), 159-193.
Fassò F.; Galasso S.; Ponno A. Point spectra and normal modes of the Rayleigh loaded string with damping. Theoretical and Applied Mechanics 52 (2025), 17-37.
Bessi U. Hodge theory on the harmonic gasket and other fractals. To appear in Nonlinear Analysis, Theory, Methods and Applications (2025).
Barutello V.; Cherubini A.; De Blasi, I. Exploration of Billiards with Keplerian Potential, Nonlinearity, Volume 38, Number 5 055004, (2025).
Barutello V.; Canneori G. M.; Ciccarelli R.; Terracini S.; Bergomi, M. G.; Vertechi P.; Ferrario D. L. Equivariant optimisation for the gravitational -body problem: A computational factory of symmetric orbits. Communications in Nonlinear Science and Numerical SimulationVolume 152, Part B, (2026), 109180.
Baracco L.; Bernardi O.; Fierobe C. Starting the study of outer length billiards. To appear in Pacific Journal of Mathematics.
Barbieri S; Biasco, L.; Chierchia L.; Zaccaria D. Singular KAM Theory for Convex Hamiltonian Systems. Regular and Chaotic Dynamics, (2025), vol. 30, no. 4, pp. 538-549.
Pozza, M. Large time behavior of solutions to Hamilton-Jacobi equations on networks. In: Nonlinear Differential Equations and Applications NoDEA 32.6 (2025).
