This article is cited in 3 papers

On symmetry breaking bifurcations in reversible systems

L. M. Lerman^ab, D. V. Turaev<sup>c

a</sup> Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod, pr. Gagarina. 23, Nizhnii Novgorod, 603950, Russia
^b N. I. Lobachevski State University of Nizhni Novgorod, Faculty of Mechanics and Mathematics, pr. Gagarina. 23, Nizhnii Novgorod, 603950, Russia
^c Department of Mathematics, Imperial College of Science, Technology and Medicine, London SW7 2AZ

Abstract: We review results on local bifurcations in reversible systems (flows and diffeomorphisms) which lead to the creation of pairs attractor–repellor at bifurcations from symmetric equilibria (for flows) and fixed points (for diffeomorphisms). We consider bifurcations of co-dimension 1 in systems of small dimensions (2,3, and 4).

Keywords: reversible system, reversible diffeomorphism, bifurcation, symmetric equilibrium, symmetric fixed point, loss of symmetry.

UDC: 517.938

MSC: 34С23, 34С14, 37G05, 37G40

Received: 20.05.2012