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Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

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Abstract

This paper is a sequel to “Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians”, in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrableGevrey Hamiltonians at a quasiperiodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

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  1. Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193, Bellaterra, Barcelona, Spain

    Abed Bounemoura

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  1. Abed Bounemoura
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Correspondence to Abed Bounemoura.

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Bounemoura, A. Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians. Regul. Chaot. Dyn. 18, 261–276 (2013). https://doi.org/10.1134/S1560354713030052

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  • DOI: https://doi.org/10.1134/S1560354713030052

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