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Slow entropy and symplectomorphisms of cotangent bundles

2004/04/01 by Urs Frauenfelder, Frauenfelder, Urs, Felix Schlenk +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #math.DS #math.SG

paper · pdf · doi:10.48550/arxiv.math/0404017

46 pages, 3 figures

arxiv created 2004/04/01 · openalex publication_date 2004/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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