Affiliation:
1. Department of Mathematics, Shandong University, Jinan, Shandong 250100, China
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.
Funder
National Natural Science Foundation of China
Subject
Applied Mathematics,Analysis