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Distribution of maps with transversal homoclinic orbits in a continuous map space. (English) Zbl 1223.37031

Summary: This paper is concerned with the distribution of maps with transversal homoclinic orbits in a space which consists of continuous maps defined in a closed and bounded set of a Banach space. By the transversal homoclinic theorem it is shown that this space contains a dense set of maps that have transversal homoclinic orbits and are chaotic in the sense of both Li-Yorke and Devaney with positive topological entropy.

MSC:

37C29 Homoclinic and heteroclinic orbits for dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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