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A numerical procedure for finding accessible trajectories on basin boundaries. (English) Zbl 0739.58038
Authors abstract: “In dynamical systems examples are common in which two or more attractors coexist, and in such cases the basin boundary is non- empty. The basin boundary is either smooth or fractal (that is, it has a Cantor-like structure). When there are horseshoes in the basin boundary, the basin boundary is fractal. A relatively small subset of a fractal basin boundary is said to be ‘accessible’ from a basin. However, these accessible points play an important role in the dynamics and, especially, in showing how the dynamics change as parameters are varied. The purpose of this paper is to present a numerical procedure that enables us to produce trajectories lying in this accessible set on the basin boundary, and we prove that this procedure is valid in certain hyperbolic systems.”.

MSC:
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
65Q05 Numerical methods for functional equations (MSC2000)
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