A simple proof of the Conley conjecture for Hamiltonian diffeomorphisms $C^1$-close to the identity

Details A simple proof of the Conley conjecture for Hamiltonian diffeomorphisms $C^1$-close to the identity A simple proof of the Conley conjecture for Hamiltonian diffeomorphisms $C^1$-close to the identity

2011-02-10

arxiv.org/abs/1102.2021v2

Mathematics

Symplectic Geometry

16 pages

Scientific paper

We provide a new simple proof of the Conley conjecture for standard
symplectic tori, asserting that each Hamiltonian diffeomorphism $\phi$ admits
infinitely many periodic points corresponding to contractible periodic orbits,
under the further assumption that $\phi$ is $C^1$-close to the identity. Our
argument is based on generating functions.

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