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Pré-Publication, Document De Travail Année : 2021

Instabilities for analytic quasi-periodic invariant tori

Gerard Farré
  • Fonction : Auteur

Résumé

We prove the existence of real analytic Hamiltonians with topologically unstable quasi-periodic invariant tori. Using various versions of our examples, we solve the following problems in the stability theory of analytic quasi-periodic motion: $\quad i)$ Show the existence of topologically unstable tori of arbitrary frequency. Moreover, the Birkhoff Normal Form at the invariant torus can be chosen to be convergent, equal to a planar or non-planar polynomial. $\quad ii)$ Show the optimality of the exponential stability for Diophantine tori. ' $\quad iii)$ Show the existence of real analytic Hamiltonians that are integrable on half of the phase space, and such that all orbits on the other half accumulate at infinity. $\quad iv)$ For sufficiently Liouville vectors, obtain invariant tori that are not accumulated by a positive measure set of quasi-periodic invariant tori.

Dates et versions

hal-03456725 , version 1 (30-11-2021)

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Bassam Fayad, Gerard Farré. Instabilities for analytic quasi-periodic invariant tori. 2021. ⟨hal-03456725⟩
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