Abstract:The survey is devoted to the topological dynamics of maps defined on one-dimensional continua such as a closed interval, a circle, finite graphs (for instance, finite trees), or dendrites (locally connected continua without subsets homeomorphic to a circle). Connections between the periodic behaviour of trajectories, the existence of a horseshoe and homoclinic trajectories, and the positivity of topological entropy are investigated. Necessary and sufficient conditions for entropy chaos in continuous maps of an… Show more
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