Breakdown of symmetry in reversible systems

Lev M. Lerman; Dimitry Turaev

doi:10.1134/S1560354712030082

Breakdown of symmetry in reversible systems

Lev M. Lerman, Dimitry Turaev

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

22 Scopus citations

Abstract

We review results on local bifurcations of codimension 1 in reversible systems (flows and diffeomorphisms) which lead to the birth of attractor-repeller pairs from symmetric equilibria (for flows) or periodic points (for diffeomorphisms).

Original language	English
Pages (from-to)	318-336
Number of pages	19
Journal	Regular and Chaotic Dynamics
Volume	17
Issue number	3-4
DOIs	https://doi.org/10.1134/S1560354712030082
State	Published - 1 Jan 2012
Externally published	Yes

Keywords

bifurcation
equilibrium state
periodic point
reversible diffeomorphism
reversible system
symmetry

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1134/S1560354712030082

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title = "Breakdown of symmetry in reversible systems",

abstract = "We review results on local bifurcations of codimension 1 in reversible systems (flows and diffeomorphisms) which lead to the birth of attractor-repeller pairs from symmetric equilibria (for flows) or periodic points (for diffeomorphisms).",

keywords = "bifurcation, equilibrium state, periodic point, reversible diffeomorphism, reversible system, symmetry",

author = "Lerman, {Lev M.} and Dimitry Turaev",

note = "Funding Information: This work was partly RF Government grant Funding Information: The authors are grateful to S. V. Gonchenko for useful discussions. supported by grants 10-01-00429a and 11-01-00001a of RFBR, by the 11.G34.31.0039, and by grant RPG-279 of the Leverhulme Trust.",

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language = "English",

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AU - Lerman, Lev M.

AU - Turaev, Dimitry

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PY - 2012/1/1

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N2 - We review results on local bifurcations of codimension 1 in reversible systems (flows and diffeomorphisms) which lead to the birth of attractor-repeller pairs from symmetric equilibria (for flows) or periodic points (for diffeomorphisms).

AB - We review results on local bifurcations of codimension 1 in reversible systems (flows and diffeomorphisms) which lead to the birth of attractor-repeller pairs from symmetric equilibria (for flows) or periodic points (for diffeomorphisms).

KW - bifurcation

KW - equilibrium state

KW - periodic point

KW - reversible diffeomorphism

KW - reversible system

KW - symmetry

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U2 - 10.1134/S1560354712030082

DO - 10.1134/S1560354712030082

M3 - Review article

AN - SCOPUS:84865571815

SN - 1560-3547

VL - 17

SP - 318

EP - 336

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

IS - 3-4

ER -

Breakdown of symmetry in reversible systems

Abstract

Keywords

ASJC Scopus subject areas

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