Universality with respect to omega-limit sets

作者：Chudziak Jacek; Garcia Guirao Juan Luis; Snoha L'ubomir; Spitalsky Vladimir^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 71(5-6): 1485-1495.

DOI：10.1016/j.na.2008.12.034

• omega-limit set
• Universal system
• Graph
• Dendrite
• Cantor set

A discrete dynamical system on a compact metric space X is called universal (with respect to omega-limit sets) if, among its omega-limit sets, there is a homeomorphic copy of any omega-limit set of any dynamical system on X. By a result of Pokluda and Smital the unit interval admits a universal system. In this paper, we study the problem of the existence of universal systems on Cantor spaces, graphs, dendrites and higher-dimensional spaces.

• 出版日期2009-9-1