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.
Qiuju Xing. Yuming Shi. "Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space." Abstr. Appl. Anal. 2011 1 - 11, 2011. https://doi.org/10.1155/2011/520273