Chaos induced by regular snap-back repellers |
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| Authors: | Yuming Shi Pei Yu |
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| Affiliation: | a Department of Mathematics, Shandong University, Jinan, Shandong 250100, PR China
b Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada |
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| Abstract: | 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 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. |
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| Keywords: | Chaos Snap-back repeller Coupled-expanding map |
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