Annales Henri Poincaré

, Volume 13, Issue 4, pp 857–868

Optimal Stability and Instability for Near-Linear Hamiltonians


DOI: 10.1007/s00023-011-0137-9

Cite this article as:
Bounemoura, A. Ann. Henri Poincaré (2012) 13: 857. doi:10.1007/s00023-011-0137-9


In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover, in the same spirit as the notion of KAM stable integrable Hamiltonians, we will introduce a notion of effectively stable integrable Hamiltonians, conjecture a characterization of these Hamiltonians and show that our result proves this conjecture in the linear case.

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© Springer Basel AG 2011

Authors and Affiliations

  1. 1.IMPARio de JaneiroBrazil

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