Hofer's distance between eggbeaters and autonomous Hamiltonian diffeomorphisms on surfaces

2022/05/31 by Michael Khanevsky, Khanevsky, Michael
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2205.15806

Abstract

Let Σ be a compact surface of genus g ≥ 1 equipped with an area form. We construct eggbeater Hamiltonian diffeomorphisms which lie arbitrarily far in the Hofer metric from the set of autonomous Hamiltonians. This result is already known for g ≥ 2 (our argument provides an alternative, very simple construction compared to previous publications) while the case g = 1 is new.

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