Geometric and Functional Analysis

, Volume 20, Issue 6, pp 1307–1316 | Cite as

On a Theorem Due to Birkhoff

Article

Abstract

The manifold M being closed and connected, we prove that every submanifold of T*M that is Hamiltonianly isotopic to the zero-section and that is invariant by a Tonelli flow is a graph.

Keywords and phrases

Lagrangian sub-manifolds Hamiltonian and Lagrangian dynamics weak KAM theory 

2010 Mathematics Subject Classification

37J50 70H20 53D12 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Laboratoire d’Analyse non linéaire et Géométrie (EA 2151)Université d’Avignon et des Pays de VaucluseAvignonFrance

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