Scrambled sets and chain recurrence points of generic graph maps

Authors：Feng, Jiahui; Kuang, Rui^*

Source：JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2022, 28(11-12): 1507-1518.

DOI：10.1080/10236198.2022.2159397

• Graph maps
• generic properties
• scrambled sets
• chain recurrence
• Hausdorff dimension

In this paper two generic properties are presented for graph maps. Let C(X, X) be the space of continuous maps from the topological graph X into itself, equipped with the topology of uniform conver-gence. Then there is a residual subset C subset of C(X, X) such that for every f is an element of C, all the scrambled sets of f, as well as the set of chain recurrence points of f, are nowhere dense and of zero Hausdorff dimension.

• Institution
  汕头大学