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Chaos induced by regular snap-back repellers. (English) Zbl 1131.37023
Summary: This paper is concerned with chaos induced by regular snap-back repellers. One new criterion of chaos induced by strictly coupled-expanding maps in compact sets of metric spaces is established. By employing this criterion, the nondegenerateness assumption in the Marotto theorem established in 1978 [F. R. Marotto, ibid. 63, 199–223 (1978; Zbl 0381.58004)] is weakened. In addition, it is proved that a regular snap-back repeller and a regular homoclinic orbit to a regular expanding fixed point in finite-dimensional spaces imply chaos in the sense of Li-Yorke. An illustrative example is provided with computer simulations.
37B25Lyapunov functions and stability; attractors, repellers
37D45Strange attractors, chaotic dynamics
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