Results 11 to 20 of about 73 (68)

Katsura–Exel–Pardo groupoids and the AH conjecture

Journal of the London Mathematical Society, Volume 104, Issue 5, Page 2240-2259, December 2021., 2021
Abstract It is proven that Matui's AH conjecture is true for Katsura–Exel–Pardo groupoids GA,B associated to integral matrices A and B. This conjecture relates the topological full group of an ample groupoid with the homology groups of the groupoid. We also give a criterion under which the topological full group [[GA,B]] is finitely generated.
Petter Nyland, Eduard Ortega
wiley   +1 more source

A Billingsley type theorem for Bowen topological entropy of nonautonomous dynamical systems

Open Mathematics, 2022
This article is devoted to the study of the Bowen topological entropy for nonautonomous dynamical systems, which is an extension of the classical definition of Bowen topological entropy. We show that the Bowen topological entropy can be determined by the
Zhang Bin, Liu Lei
doaj   +1 more source

A bridge theorem for the entropy of semigroup actions

Topological Algebra and its Applications, 2020
The topological entropy of a semigroup action on a totally disconnected locally compact abelian group coincides with the algebraic entropy of the dual action.
Bruno Anna Giordano
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The boundary of chaos for interval mappings

Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1427-1467, December 2020., 2020
Abstract A goal in the study of dynamics on the interval is to understand the transition to positive topological entropy. There is a conjecture from the 1980s that the only route to positive topological entropy is through a cascade of period doubling bifurcations. We prove this conjecture in natural families of smooth interval maps, and use it to study
Trevor Clark, Sofía Trejo
wiley   +1 more source

Topological mixing properties of rank‐one subshifts

Transactions of the London Mathematical Society, Volume 6, Issue 1, Page 1-21, December 2019., 2019
Abstract We study topological mixing properties and the maximal equicontinuous factor of rank‐one subshifts as topological dynamical systems. We show that the maximal equicontinuous factor of a rank‐one subshift is finite. We also determine all the finite factors of a rank‐one shift with a condition involving the cutting and spacer parameters. For rank‐
Su Gao, Caleb Ziegler
wiley   +1 more source

Relative Nielsen Numbers, Braids and Periodic Segments

Advanced Nonlinear Studies, 2017
The aim of this paper is to establish a connection between the method of period segments and the relative Nielsen fixed point theory. We prove that if W is a periodic segment over [0,T]{[0,T]} for the T-periodic semi-process Φ, then the Poincaré map P ...
Wójcik Klaudiusz
doaj   +1 more source

Common periodic points for a class of continuous commuting mappings on an interval

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 16, Page 1043-1046, 2003., 2003
The existence of common periodic points for a family of continuous commuting self‐mappings on an interval is proved and two illustrative examples are given in support of our theorem and definition.
Shin Min Kang, Weili Wang
wiley   +1 more source

Equicontinuity of iterates of circle maps

International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 453-458, 1998., 1998
Let f be a continuous map of the circle to itself. Necessary and sufficient conditions are given for the family ofiterates to be equicontinuous.
Antonios Valaristos
wiley   +1 more source

Localization of the Chain Recurrent set using Shape theory and Symbolical Dynamics

Topological Algebra and its Applications, 2019
The main aim of this paper is localization of the chain recurrent set in shape theoretical framework. Namely, using the intrinsic approach to shape from [1] we present a result which claims that under certain conditions the chain recurrent set preserves ...
Shoptrajanov M.
doaj   +1 more source

Attractors of dynamical systems in locally compact spaces

Open Mathematics, 2019
In this article the properties of attractors of dynamical systems in locally compact metric space are discussed. Existing conditions of attractors and related results are obtained by the near isolating block which we present.
Li Gang, Gao Yuxia
doaj   +1 more source