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Ergodic Theory and Dynamical Systems (1)

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1 results

Generic chaos on dendrites
Part of
- Topological dynamics
- Low-dimensional dynamical systems
ĽUBOMÍR SNOHA, VLADIMÍR ŠPITALSKÝ, MICHAL TAKÁCS
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 6 / June 2022

Published online by Cambridge University Press:

19 March 2021, pp. 2108-2150

Print publication:

June 2022
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We characterize dendrites D such that a continuous selfmap of D is generically chaotic (in the sense of Lasota) if and only if it is generically ${\varepsilon }$ -chaotic for some ${\varepsilon }>0$ . In other words, we characterize dendrites on which generic chaos of a continuous map can be described in terms of the behaviour of subdendrites with non-empty interiors under iterates of the map. A dendrite D belongs to this class if and only if it is completely regular, with all points of finite order (that is, if and only if D contains neither a copy of the Riemann dendrite nor a copy of the $\omega $ -star).