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Distributional chaos of time-varying discrete dynamical systems

Lidong Wang, Yingnan Li, Yuelin Gao, Heng Liu (2013)

Annales Polonici Mathematici

This paper is concerned with distributional chaos of time-varying discrete systems in metric spaces. Some basic concepts are introduced for general time-varying systems, including sequentially distributive chaos, weak mixing, and mixing. We give an example of sequentially distributive chaos of finite-dimensional linear time-varying dynamical systems, which is not distributively chaotic of type i (DCi for short, i = 1, 2). We also prove that two uniformly topological equiconjugate time-varying systems...

Dynamics of commuting homeomorphisms of chainable continua

Christopher Mouron (2010)

Colloquium Mathematicae

A chainable continuum, X, and homeomorphisms, p,q: X → X, are constructed with the following properties: (1) p ∘ q = q ∘ p, (2) p, q have simple dynamics, (3) p ∘ q is a positively continuum-wise fully expansive homeomorphism that has positive entropy and is chaotic in the sense of Devaney and in the sense of Li and Yorke.

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