Abstract and Applied Analysis

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

Qiuju Xing and Yuming Shi

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 520273, 11 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171199

Digital Object Identifier
doi:10.1155/2011/520273

Mathematical Reviews number (MathSciNet)
MR2817256

Zentralblatt MATH identifier
1223.37031

Citation

Xing, Qiuju; Shi, Yuming. Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space. Abstr. Appl. Anal. 2011 (2011), Article ID 520273, 11 pages. doi:10.1155/2011/520273. https://projecteuclid.org/euclid.aaa/1313171199


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