Slow entropy and symplectomorphisms of cotangent bundles

Details Slow entropy and symplectomorphisms of cotangent bundles Slow entropy and symplectomorphisms of cotangent bundles

2004-04-01

arxiv.org/abs/math/0404017v1

Mathematics

Symplectic Geometry

46 pages, 3 figures

Scientific paper

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.

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