2D universality of period-doubling bifurcations in 3D conservative reversible mappings

Stavros Komineas, Michael N. Vrahatis, Tassos Bountis

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Infinite sequences of period-doubling bifurcations are known to occur generically (i.e. with codimension 1) not only in dissipative 1D systems but also in 2D conservative systems, described by area-preserving mappings. In this paper, we study a 3D volume-preserving, reversible mapping and show that it does possess period 2m(m=1,2,...) orbits, with stability intervals whose length decreases rapidly, with increasing m. Varying one parameter of the system we find that these orbits always bifurcate out of one another with the usual stability exchange and universal properties of period-doubling sequences of 2D-conservative maps. This raises the interesting question whether these 3D reversible maps possess an analytic integral which would render them essentially 2-dimensional.

Original languageEnglish
Pages (from-to)218-233
Number of pages16
JournalPhysica A: Statistical Mechanics and its Applications
Volume211
Issue number2-3
DOIs
Publication statusPublished - Nov 1 1994
Externally publishedYes

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Period-doubling Bifurcation
period doubling
preserving
Universality
orbits
Orbit
intervals
Conservative System
2-D Systems
Period Doubling
Dissipative Systems
Codimension
Decrease
Interval

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

2D universality of period-doubling bifurcations in 3D conservative reversible mappings. / Komineas, Stavros; Vrahatis, Michael N.; Bountis, Tassos.

In: Physica A: Statistical Mechanics and its Applications, Vol. 211, No. 2-3, 01.11.1994, p. 218-233.

Research output: Contribution to journalArticle

Komineas, Stavros ; Vrahatis, Michael N. ; Bountis, Tassos. / 2D universality of period-doubling bifurcations in 3D conservative reversible mappings. In: Physica A: Statistical Mechanics and its Applications. 1994 ; Vol. 211, No. 2-3. pp. 218-233.
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