On the asymptotic geometry of area-preserving maps

Details On the asymptotic geometry of area-preserving maps On the asymptotic geometry of area-preserving maps

1999-05-10

arxiv.org/abs/math/9905054v1

Mathematics

Differential Geometry

9 pages

Scientific paper

We study the asymptotic behaviour of 1-parameter subgroups with respect to Hofer's metric when the underlying symplectic manifold is an open surface of infinite area. We prove that, depending on the topology of the level sets of the Hamiltonian H, the distance either is bounded or behaves asymptotically linear. Moreover, the slope can be calculated explicitly as the difference of two distinguished critical values of H.

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