Non-autonomous curves on surfaces

2019/06/19 by Michael Khanevsky, Khanevsky, Michael · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DS #math.SG

paper · pdf · doi:10.48550/arxiv.1906.07884

Incorporated referee remarks

arxiv created 2021/05/31 · arxiv updated 2021/06/01

Abstract

Consider a symplectic surface Σ with two properly embedded Hamiltonian isotopic curves L and L'. Suppose g ∈ Ham (Σ) is a Hamiltonian diffeomorphism which sends L to L'. Which dynamical properties of g can be detected by the pair (L, L')? We discuss two cases where one can deduce that g is `chaotic': non-autonomous or even of positive entropy.

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