Autonomous Hamiltonian flows, Hofer's geometry and persistence modules

2014/12/29 by Leonid Polterovich, Polterovich, Leonid, Egor Shelukhin +1 · 6 citations
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DS #math.SG

paper · pdf · doi:10.48550/arxiv.1412.8277

66 pages, 6 figures; introduction expanded, small changes in the exposition

arxiv created 2015/02/19 · arxiv updated 2015/02/20

Abstract

We find robust obstructions to representing a Hamiltonian diffeomorphism as a full k-th power, k ≥ 2, and in particular, to including it into a one-parameter subgroup. The robustness is understood in the sense of Hofer's metric. Our approach is based on the theory of persistence modules applied in the context of filtered Floer homology. We present applications to geometry and dynamics of Hamiltonian diffeomorphisms.

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