Non-autonomous curves on surfaces

Michael Khanevsky

doi:https://doi.org/10.3934/jmd.2021010

Non-autonomous curves on surfaces

Michael Khanevsky

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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 present two scenarios where one can deduce that g is “chaotic:” non-autonomous or even of positive entropy.

Original language	English
Pages (from-to)	305-317
Number of pages	13
Journal	Journal of Modern Dynamics
Volume	17
DOIs	https://doi.org/10.3934/jmd.2021010
State	Published - 2021

Keywords

Hamiltonian dynamics
Non-autonomous diffeomorphisms

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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https://doi.org/10.3934/jmd.2021010

Cite this

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title = "Non-autonomous curves on surfaces",

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 present two scenarios where one can deduce that g is “chaotic:” non-autonomous or even of positive entropy.",

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AB - 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 present two scenarios where one can deduce that g is “chaotic:” non-autonomous or even of positive entropy.

KW - Hamiltonian dynamics

KW - Non-autonomous diffeomorphisms

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U2 - https://doi.org/10.3934/jmd.2021010

DO - https://doi.org/10.3934/jmd.2021010

M3 - مقالة

SN - 1930-5311

VL - 17

SP - 305

EP - 317

JO - Journal of Modern Dynamics

JF - Journal of Modern Dynamics

ER -

Non-autonomous curves on surfaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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