On the asymptotic geometry of area-preserving maps

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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.
9 pages

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Differential Geometry, Symplectic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/78475

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9905054
 http://arxiv.org/abs/math/9905054

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arXiv