Repellers, semi-attractors, and long-lived chaotic transients. (English) Zbl 0597.58017

Summary: We study the chaotic transients observed in many deterministic systems. In general, they are related to strange repellers (or ”semi-attractors”, if they are repelling in some and attracting in other directions). We propose formulas relating the average lifetime of the transient to dimensions of the repeller, and to Lyapunov exponents of the flow on it. The formulas are tested numerically in a number of cases.


37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
26A18 Iteration of real functions in one variable
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