Dwelltime Analysis of Symmetry-Breaking Dynamical Systems

Abstract

Dwelltime analysis is known to characterize saddles giving rise to chaotic scattering. In the present paper it is used to characterize the dependence on initial conditions of the attractor approached by a trajectory in dissipative systems described by one-dimensional, noninvertible mappings which show symmetry breaking. There may be symmetry-related attractors in these systems, and which attractor is approached may depend sensitively on the initial conditions. Dwell-time analysis is useful in this context because it allows to visualize in another way the repellers on the basin boundary which cause this sensitive dependence. © Verlag der Zeitschrift für Naturforschung