Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds

Details Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds

2005-10-14

arxiv.org/abs/math/0510292v1

Mathematics

Dynamical Systems

Scientific paper

This paper is devoted to the proof of almost global existence results for
Klein-Gordon equations on Zoll manifolds (e.g. spheres of arbitrary dimension)
with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The
proof relies on Birkhoff normal form methods and on the specific distribution
of eigenvalues of the laplacian perturbed by a potential on Zoll manifolds.

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