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arXiv · 2408.08854

A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization

Lev Buhovsky·Ben Feuerstein·Leonid Polterovich·Egor Shelukhin
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Abstract

We prove that autonomous Hamiltonian flows on the two-sphere exhibit the following dichotomy: the Hofer norm either grows linearly or is bounded in time by a universal constant C. Our approach involves a new technique, Hamiltonian symmetrization. Essentially, we prove that every autonomous Hamiltonian diffeomorphism is conjugate to an element C-close in the Hofer metric to one generated by a function of the height.

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Lev Buhovsky, Ben Feuerstein, Leonid Polterovich, Egor Shelukhin. 2024-08-16. A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization. https://arxiv.org/abs/2408.08854

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