Dynamical Systems and Applications

Birkhoff stability and Nekhoroshev stability of elliptic equilibrium positions in Hamiltonian systems

4 Dec 2019, 09:45

55m

Auditorio Hermann Gamm (UBB, Concepcion)

Speaker

Laurent Niederman (Laboratoire Mathématiques d'Orsay and IMCCE/ASD Orsay, France)

Description

We present a survey of stability results for elliptic equilibrium positions in Hamiltonian systems under generic assumptions.
References:
Giorgilli, A., Delshams, A., Fontich, E., Galgani, L., and Simo, C., Effective Stability for a Hamiltonian System near an Elliptic Equilibrium Point, with an Application to the Restricted Three-Body Problem, J. Differential Equations, 1989, vol. 77, no. 1, pp. 167–198.
Niederman, L., Generic super-exponential stability of elliptic equilibrium positions for symplectic vector fields, Regul. Chaotic Dyn. 18 (2013), no. 6, 719–731.
Bounemoura, A., Fayad, B., Niederman, L., Nekhoroshev estimates for steep real-analytic elliptic equilibrium points, to appear in Nonlinearity, preprint HAL https://hal.archives-ouvertes.fr/hal-02074689
Bounemoura, A., Fayad, B., Niederman, L., Super-exponential stability for generic real-analytic elliptic equilibrium points, preprint HAL https://hal.inria.fr/hal-01188980v1