Annales Henri Poincaré

, Volume 13, Issue 4, pp 857–868 | Cite as

Optimal Stability and Instability for Near-Linear Hamiltonians

  • Abed BounemouraEmail author


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.


Normal Form Hamiltonian System Integrable Hamiltonian System Optimal Stability Diophantine Condition 
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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.IMPARio de JaneiroBrazil

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