Hamiltonian loops from the ergodic point of view

Details Hamiltonian loops from the ergodic point of view Hamiltonian loops from the ergodic point of view

1998-06-29

arxiv.org/abs/math/9806152v2

Mathematics

Differential Geometry

a reference added, minor corrections; LATEX, 21 pages

Scientific paper

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.

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