Displaying similar documents to “Hamiltonian stability and subanalytic geometry”

Generic Nekhoroshev theory without small divisors

Abed Bounemoura, Laurent Niederman (2012)

Annales de l’institut Fourier

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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...

The tiered Aubry set for autonomous Lagrangian functions

Marie-Claude Arnaud (2008)

Annales de l’institut Fourier

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Let L : T M → ℝ be a Tonelli Lagrangian function (with M compact and connected and dim M ≥ 2 ). The tiered Aubry set (resp. Mañé set) 𝒜 T ( L ) (resp. 𝒩 T ( L ) ) is the union of the Aubry sets (resp. Mañé sets) 𝒜 ( L + λ ) (resp. 𝒩 ( L + λ ) ) for λ closed 1-form. Then the set 𝒩 T ( L ) is closed, connected and if dim H 1 ( M ) ≥ 2 , its intersection with any energy level is connected and chain...

Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle

Christiane Rousseau, Colin Christopher (2007)

Annales de l’institut Fourier

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We consider germs of one-parameter generic families of resonant analytic diffeomorphims and we give a complete modulus of analytic classification by means of the unfolding of the Écalle modulus. We describe the parametric resurgence phenomenon. We apply this to give a complete modulus of orbital analytic classification for the unfolding of a generic resonant saddle of a 2-dimensional vector field by means of the unfolding of its holonomy map. Here again the modulus is an unfolding of...

Systems of rays in the presence of distribution of hyperplanes

S. Janeczko (1995)

Banach Center Publications

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Horizontal systems of rays arise in the study of integral curves of Hamiltonian systems v H on T*X, which are tangent to a given distribution V of hyperplanes on X. We investigate the local properties of systems of rays for general pairs (H,V) as well as for Hamiltonians H such that the corresponding Hamiltonian vector fields v H are horizontal with respect to V. As an example we explicitly calculate the space of horizontal geodesics and the corresponding systems of rays for the canonical...