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Zbl 1131.37023
Shi, Yuming; Yu, Pei
Chaos induced by regular snap-back repellers. (English)
[J] J. Math. Anal. Appl. 337, No. 2, 1480-1494 (2008). ISSN 0022-247X

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 [{\it 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.

MSC 2000:: *37B25 Lyapunov functions and stability
37D45 Strange attractors, chaotic dynamics

Keywords: chaos; snap-back repeller; coupled-expanding map; nondegenerateness assumption

Citations: Zbl 0381.58004

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