Slow entropy and symplectomorphisms of cotangent bundles
Symplectic Geometry
2007-05-23 v1 Dynamical Systems
Abstract
We consider an entropy-type invariant which measures the polynomial volume growth of submanifolds under the iterates of a map, and we establish sharp uniform lower bounds of this invariant for the following classes of symplectomorphisms of cotangent bundles over a compact base: 1) non-identical compactly supported symplectomorphisms which are symplectically isotopic to the identity, 2) symplectomorphisms generated by classical Hamiltonian functions, 3) Dehn twist like symplectomorphisms over compact rank one symmetric spaces.
Cite
@article{arxiv.math/0404017,
title = {Slow entropy and symplectomorphisms of cotangent bundles},
author = {Urs Frauenfelder and Felix Schlenk},
journal= {arXiv preprint arXiv:math/0404017},
year = {2007}
}
Comments
46 pages, 3 figures