Seminari del Dipartimento

 

Analisi Matematica

Generic double exponential stability of invariant Lagrangian tori in Hamiltonian systems, application to KAM theory.

Laurent Niederman


22-02-2022 - 16:30
Largo San Leonardo Murialdo,1 - Pal.C

 

In a joint work with Abed Bounemoura and Bassam Fayad, we prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus for an interval of time which is doubly exponentially large with respect to the inverse of the distance to the torus.

These results extend in a generic setting a theorem of Morbidelli and Giorgilli valid in the convex case.

 We also prove that for an arbitrary small perturbation of a generic integrable Hamiltonian system, there is a set of almost full positive Lebesgue measure of KAM tori which are doubly exponentially stable.

 Similar theorems are also proved in the vicinity of an elliptic equilibrium point in a Hamiltonian system.

 Our results hold true for real-analytic but more generally for Gevrey smooth systems.

References:
1. Super-exponential stability for generic real-analytic elliptic equilibrium points, Advances in Math., vol. 366, 2020.
2. Nekhoroshev estimates for steep real-analytic elliptic equilibrium points, Nonlinearity, vol. 33(1), pp. 1-33, 2020.
3. Superexponential Stability of Quasi-Periodic Motion in Hamiltonian Systems, Commun. Math. Phys., vol. 350(1), pp. 361-386, 2017.

Il seminario avrà luogo in presenza presso il Dipartimento di Matematica e Fisica
Aula 211, Palazzina C, L.go S.L. Murialdo 1
org: BIASCO Luca

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