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.
Original language | Undefined |
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Pages (from-to) | 625-662 |
Number of pages | 38 |
Journal | Physica A |
Volume | 164 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1990 |
Keywords
- IR-72890
- METIS-129598