Journal
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL
Volume 26, Issue 4, Pages 519-535Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/14689367.2011.627836
Keywords
chaos; distribution; continuous map space; coupled-expanding map; snap-back repeller
Categories
Funding
- RFDP of Higher Education of China [20100131110024]
- NNSF of China [11071143]
- NNSF of Shandong Province [ZR2011AM002]
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This article is concerned with distribution of several kinds of chaotic maps in a continuous map space, in which the maps are defined in a closed bounded set of a Banach space. It is shown that the map space contains a dense set of maps that are strictly coupled-expanding, have nondegenerate and regular snap-back repellers, have nondegenerate and regular homoclinic orbits to repellers, and consequently that are chaotic in the sense of Devaney as well as in the original sense of Li-Yorke, and have the topological entropy larger than any given positive constant. Further, in the finite-dimensional case, there exists a dense residual set of the map space such that every map f in the set is strictly coupled-expanding in k pairwise disjoint compact sets for any given integer k >= 2, is chaotic in the sense of Li-Yorke and has the infinite topological entropy and a nontrivial invariant measure.
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