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arXiv · 1405.7931

On the $L^p$-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky·Egor Shelukhin
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Abstract

We prove a number of results on the interrelation between the $L^p$-metric on the group of Hamiltonian diffeomorphisms of surfaces and the subset of all autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms of all surfaces of genus $g\neq 1$ lying arbitrarily $L^p$-far from this subset; answering a variant of a question of Polterovich for the $L^p$-metric.

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Michael Brandenbursky, Egor Shelukhin. 2014-06-16. On the $L^p$-geometry of autonomous Hamiltonian diffeomorphisms of surfaces. https://arxiv.org/abs/1405.7931

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