Page 1

Displaying 1 – 11 of 11

Showing per page

Generic Nekhoroshev theory without small divisors

Abed Bounemoura, Laurent Niederman (2012)

Annales de l’institut Fourier

In this article, we present a new approach of Nekhoroshev’s theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak, it combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of...

Stability is not open

Kai Cieliebak, Urs Frauenfelder, Gabriel P. Paternain (2010)

Annales de l’institut Fourier

We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.

Stability of higher order singular points of Poisson manifolds and Lie algebroids

Jean-Paul Dufour, Aïssa Wade (2006)

Annales de l’institut Fourier

We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first-order approximation (not necessarily linear) of a given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical Lichnerowicz-Poisson cohomology and the deformation cohomology for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide several examples of stable singular...

Currently displaying 1 – 11 of 11

Page 1