A generalization of classical action of Hamiltonian diffeomorphisms to Hamiltonian homeomorphisms on fixed points

Details A generalization of classical action of Hamiltonian diffeomorphisms to Hamiltonian homeomorphisms on fixed points A generalization of classical action of Hamiltonian diffeomorphisms to Hamiltonian homeomorphisms on fixed points

2011-06-06

arxiv.org/abs/1106.1104v4

Mathematics

Dynamical Systems

56pp

Scientific paper

We define boundedness properties on the contractible fixed points set of the time-one map of an identity isotopy on an oriented closed surface with genus $g\geq1$. In symplectic geometry, a classical object is the notion of action function, defined on the set of contractible fixed points of the time-one map of a Hamiltonian isotopy. We give a dynamical interpretation of this function that permits us to generalize it in the case of a homeomorphism isotopic to identity that preserves a Borel finite measure of rotation vector zero, provided that a boundedness condition is satisfied. We give some properties of the generalized action.

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