Bifurcations of symmetric periodic orbits via Floer homology

Joontae Kim; Seongchan Kim; Myeonggi Kwon

doi:10.1007/s00526-020-01757-x

Bifurcations of symmetric periodic orbits via Floer homology

Joontae Kim
, Seongchan Kim^*
, Myeonggi Kwon

^*Corresponding author for this work

Department of Mathematics Education

Korea Institute for Advanced Study
University of Neuchatel
Ruhr University Bochum

Research output: Contribution to journal › Journal article › peer-review

2 Scopus citations

Abstract

We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct circular orbits in the rotating Kepler problem and observe bifurcations of torus-type orbits. Our setup is motivated by numerical work of Hénon on Hill’s lunar problem.

Original language	English
Article number	101
Journal	Calculus of Variations and Partial Differential Equations
Volume	59
Issue number	3
DOIs	https://doi.org/10.1007/s00526-020-01757-x
State	Published - 2020.06.1

Keywords

Bifurcation
Families of symmetric periodic orbits
Reversible Hamiltonian systems

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10.1007/s00526-020-01757-x

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title = "Bifurcations of symmetric periodic orbits via Floer homology",

abstract = "We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct circular orbits in the rotating Kepler problem and observe bifurcations of torus-type orbits. Our setup is motivated by numerical work of H{\'e}non on Hill{\textquoteright}s lunar problem.",

keywords = "Bifurcation, Families of symmetric periodic orbits, Reversible Hamiltonian systems",

author = "Joontae Kim and Seongchan Kim and Myeonggi Kwon",

note = "Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",

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T1 - Bifurcations of symmetric periodic orbits via Floer homology

AU - Kim, Joontae

AU - Kim, Seongchan

AU - Kwon, Myeonggi

PY - 2020/6/1

Y1 - 2020/6/1

N2 - We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct circular orbits in the rotating Kepler problem and observe bifurcations of torus-type orbits. Our setup is motivated by numerical work of Hénon on Hill’s lunar problem.

AB - We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct circular orbits in the rotating Kepler problem and observe bifurcations of torus-type orbits. Our setup is motivated by numerical work of Hénon on Hill’s lunar problem.

KW - Bifurcation

KW - Families of symmetric periodic orbits

KW - Reversible Hamiltonian systems

UR - https://www.scopus.com/pages/publications/85085050552

U2 - 10.1007/s00526-020-01757-x

DO - 10.1007/s00526-020-01757-x

M3 - Journal article

AN - SCOPUS:85085050552

SN - 0944-2669

VL - 59

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 3

M1 - 101

ER -

Bifurcations of symmetric periodic orbits via Floer homology

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Keywords

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