Displaying similar documents to “Stability is not open”

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...

Formal geometric quantization

Paul-Émile Paradan (2009)

Annales de l’institut Fourier

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Let K be a compact Lie group acting in a Hamiltonian way on a symplectic manifold ( M , Ω ) which is pre-quantized by a Kostant-Souriau line bundle. We suppose here that the moment map Φ is proper so that the reduced space M μ : = Φ - 1 ( K · μ ) / K is compact for all μ . Then, we can define the “formal geometric quantization” of M as 𝒬 K - ( M ) : = μ K ^ 𝒬 ( M μ ) V μ K . The aim of this article is to study the functorial properties of the assignment ( M , K ) 𝒬 K - ( M ) .

Regular projectively Anosov flows on three-dimensional manifolds

Masayuki Asaoka (2010)

Annales de l’institut Fourier

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We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of T 2 × I -models. We also apply our method to rigidity problems of some group actions.

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 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...