Affiliation:
1. Mathematical Institute in Opava, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava, Czech Republic
Abstract
We consider various kinds of chaotic behavior of continuous maps on compact metric spaces: the positivity of topological entropy, the existence of a horseshoe, the existence of a homoclinic trajectory (or perhaps, an eventually periodic homoclinic trajectory), three levels of Li–Yorke chaos, three levels of ω-chaos and distributional chaos of type 1. The relations between these properties are known when the space is an interval. We survey the known results in the case of trees, graphs and dendrites.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)
Cited by
11 articles.
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1. Shadowing, transitivity and a variation of omega-chaos;Journal of Mathematical Analysis and Applications;2024-08
2. One-dimensional dynamical systems;Russian Mathematical Surveys;2021-10-01
3. Generic chaos on dendrites;Ergodic Theory and Dynamical Systems;2021-03-19
4. Dynamics on dendrites with closed endpoint sets;Nonlinear Analysis;2020-06
5. ω-Chaos Without Infinite LY-Scrambled Set on Gehman Dendrite;International Journal of Bifurcation and Chaos;2019-05