Hamiltonian loops from the ergodic point of view

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The paper provides a link between ergodic theory and symplectic topology. A classical notion of ergodic theory is a skew product map associated with a loop in a group of transformations. We study skew products which come from loops in the group of Hamiltonian diffeomorphisms of a symplectic manifold. Our main question is which homotopy classes of loops can be represented by strictly ergodic skew products. We prove an existence result, and find an obstruction which arises from Hofer's geometry on the group of Hamiltonian diffeomorphisms.
a reference added, minor corrections; LATEX, 21 pages

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Differential Geometry, Dynamical Systems, Symplectic Geometry, 58Dxx (Primary) 58F05 28D05 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/77098

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9806152
 http://arxiv.org/abs/math/9806152

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arXiv