Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space

Qiuju Xing and Yuming Shi

Abstract and Applied Analysis, 2011, vol. 2011, 1-11

Abstract:

This paper is concerned with distribution of maps with transversal homoclinic orbits in a continuous map 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 the map 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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:520273

DOI: 10.1155/2011/520273

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