A multidimensional Birkhoff theorem for time-dependent Tonelli Hamiltonians

被引：0

作者：

Arnaud, Marie-Claude ^{[1
]}

Venturelli, Andrea ^{[1
]}

机构：

[1] Avignon Univ, Lab Math Avignon EA 2151, F-84018 Avignon, France

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2017年 / 56卷 / 04期

关键词：

GENERATING-FUNCTIONS; GEOMETRY; SYSTEMS; INTERSECTIONS;

D O I：

10.1007/s00526-017-1210-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M be a closed and connected manifold, H : T*M x R/Z -> R a Tonelli 1-periodic Hamiltonian and L subset of T * M a Lagrangian submanifold Hamiltonianly isotopic to the zero section. We prove that if L is invariant by the time- one map of H, then L is a graph over M. An interesting consequence in the autonomous case is that in this case, L is invariant by all the time t maps of the Hamiltonian flow of H.

引用

页数：27

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