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

2014/05/30 by Michael Brandenbursky, Brandenbursky, Michael, Egor Shelukhin +1
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.1405.7931

17 pages, 2 figures. Contains results from arXiv:1305.2757

openalex publication_date 2014/05/30 · arxiv created 2014/06/16 · arxiv updated 2014/06/17 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

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≠ 1 lying arbitrarily L^p-far from this subset; answering a variant of a question of Polterovich for the L^p-metric.

Citations

• On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces

Cited by

• On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces

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