DYNAMICS OF MONOTONE GRAPH, DENDRITE AND DENDROID MAPS

DOI10.1142/S0218127411030465zbMath1258.37049MaRDI QIDQ4908427

Issam Naghmouchi

Publication date: 5 March 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

graph\(\omega\)-limit setdendritedendroidgraph mapLi-Yorke pair

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Topological spaces of dimension (leq 1); curves, dendrites (54F50) Continua theory in dynamics (37B45) Dynamical systems involving maps of trees and graphs (37E25)

Related Items (20)

Invariant scrambled sets, uniform rigidity and weak mixing ⋮ Monotone Maps on Dendrites ⋮ On totally periodic \(\omega \)-limit sets for monotone maps on regular curves ⋮ On regular curve homeomorphisms without periodic points ⋮ Dynamics of monotone maps on regular curves ⋮ Homeomorphism of hereditarily locally connected continua ⋮ Nonwandering sets and special \(\alpha\)-limit sets of monotone maps on regular curves ⋮ On limit sets of monotone maps on dendroids ⋮ Topological size of scrambled sets for local dendrite maps ⋮ Dynamical properties of monotone dendrite maps ⋮ Chain recurrent points of monotone graph maps and CR-Pm property on local dendrites ⋮ On limit sets of monotone maps on regular curves ⋮ Möbius disjointness conjecture for local dendrite maps ⋮ On totally periodic \(\omega\)-limit sets in regular continua ⋮ \(\omega\)-limit sets for monotone local dendrite maps ⋮ Minimal sets for group actions on dendrites ⋮ Invariant Sets for Monotone Local Dendrite Maps ⋮ Pointwise-recurrent dendrite maps ⋮ AUSLANDER–YORKE CHAOS FOR GROUP ACTIONS ON DENDRITES ⋮ Remarks on the existence of periodic points for continuous maps on dendrites

Cites Work

• Topological entropy of maps on regular curves
• On the centre and the set of \(\omega \)-limit points of continuous maps on dendrites
• Dynamics in one dimension
• Continuous itinerary functions and dendrite maps
• Omega limit sets and distributional chaos on graphs
• The dynamics of monotone maps of dendrites
• $\overline{R} = \overline{P}$ FOR MAPS OF DENDRITES X WITH Card(End(X)) < c
• Period Three Implies Chaos
• TOWARD A THEORY OF FORCING ON MAPS OF TREES
• On the Center of Continuous Maps of Dendrites
• Minimal Sets on Graphs and Dendrites
• A note on periodic points and recurrent points of maps of dendrites

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