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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.”.

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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