On the Center of Continuous Maps of Dendrites

Recent Developments in Dynamical Systems: Three Perspectives

“…For definitions and detailed account of results see [Nadler, 1995]. Problems such as periodic structure using methods from combinatorial dynamics have been studied on circles, trees and finite graphs (see [Alsedà et al, 2000]), as well as on centers and depth of centers [Ye, 1993, Kato, 1995, Kato, 1998, Efremova & Makhrova, 2003] on trees, graphs and dendrites, and on the structure of ω-limit sets [Kocan et al, 2010, Balibrea & García Guirao, 2005, in particular, ω-limit sets on hereditarily locally connected continua [Spitalský, 2008], etc.…”

Equicontinuity of maps on a dendrite with finite branch points

“…In recent years, some properties on discrete dynamical systems on dendrites, such as the topological structure of minimal sets, the depth of the center, the topological entropies of dendrite maps, are deeply discussed by many authors (see [1,2,9,10,17,18,22,24]). The interest in these subjects is motivated in part by the fact that dendrites appear as Julia sets in complex dynamics (see [4,19]).…”