Bifurcations in two-dimensional reversible maps

T. Post, H.W. Capel, G.R.W. Quispel and J.P. Van Der Weele

Physica A: Statistical Mechanics and its Applications, 1990, vol. 164, issue 3, 625-662

Abstract: We give a treatment of the non-resonant bifurcations involving asymmetric fixed points with Jacobian J ≠ 1 in reversible mappings of the plane. These bifurcations include the saddle-node bifurcation not in the neighbourhood of a fixed point with J = 1, as well as the so-called transcritical bifurcations and generalized Rimmer bifurcations taking place at a fixed point with Jacobian J = 1. The bifurcations are illustrated by some simple examples of model maps. The Rimmer type of bifurcation, with e.g. a center point with J = 1 changing into a saddle with Jacobian J = 1, an attractor and a repeller, occurs under more general conditions, i.e. also in non-reversible mappings if only a certain order of local reversibility is satisfied. These Rimmer bifurcations are important in connection with the emergence of dissipative features in non-measure-preserving reversible dynamical systems.

Date: 1990
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/037843719090226I
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:164:y:1990:i:3:p:625-662

DOI: 10.1016/0378-4371(90)90226-I

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().