Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites

DOI10.1017/S0143385709001011zbMath1223.37022OpenAlexW4252781609MaRDI QIDQ3074752

Zdeněk Kočan, Veronika Kornecká-Kurková, Michal Málek

Publication date: 10 February 2011

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385709001011

zbMATH Keywords

entropytreehorseshoehomoclinic trajectorygraph, dendrite

Mathematics Subject Classification ID

Topological entropy (37B40) Dynamical systems involving maps of the interval (37E05) Dynamical systems involving maps of trees and graphs (37E25)

Related Items (16)

Quasi-graphs, zero entropy and measures with discrete spectrum ⋮ Dendrites and measures with discrete spectrum ⋮ The existence of a linear horseshoe of continuous maps of dendrites ⋮ Monotone Maps on Dendrites ⋮ Remarks on minimal sets on dendrites and finite graphs ⋮ Transitive dendrite map with zero entropy ⋮ Structure of dendrites admitting an existence of an arc horseshoe ⋮ Distributional Chaos and Dendrites ⋮ CHAOS ON ONE-DIMENSIONAL COMPACT METRIC SPACES ⋮ Dendrites and Chaos ⋮ Li-Yorke chaos for dendrite maps with zero topological entropy and \(\omega\)-limit sets ⋮ Horseshoes, Entropy, Homoclinic Trajectories, and Lyapunov Stability ⋮ Counterexamples of continuous maps on dendrites ⋮ Dynamics on dendrites with closed endpoint sets ⋮ Equicontinuity and Li–Yorke pairs of dendrite maps ⋮ Properties of Dynamical Systems on Dendrites and Graphs

Cites Work

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• Dynamics in one dimension
• Horseshoes, entropy and periods for graph maps
• How little is little enough?

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