Topological dynamics: Rigorous numerics via cubical homology

2012 ◽  
pp. 41-73 ◽  
Author(s):  
Marian Mrozek
Keyword(s):  
Topological Dynamics ◽  
Rigorous Numerics ◽  
Cubical Homology

scholarly journals Topological Dynamics and the Space of Continuous Mappings

2020 ◽  
Vol 1591 ◽  
pp. 012066
Author(s):  
Mohammed Nokhas Murad Kaki ◽  
Reyadh. D. Ali
Keyword(s):  
Topological Dynamics ◽  
Continuous Mappings

scholarly journals Category Theory for Autonomous and Networked Dynamical Systems

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 302 ◽  
Author(s):  
Jean-Charles Delvenne
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Ergodic Theory ◽  
Category Theory ◽  
Open Systems ◽  
Topological Dynamics ◽  
Control Problems ◽  
Natural Conditions ◽  
Discussion Paper ◽  
Open Systems Theory

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way.

Fixed Points for Dissipative-Repulsive Systems and Topological Dynamics of Mappings Defined on N-dimensional Cells

2005 ◽  
Vol 5 (3) ◽  
Author(s):  
Marina Pireddu ◽  
Fabio Zanolin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Topological Dynamics ◽  
Continuous Mappings ◽  
Expansion Condition ◽  
Dimensional Cell

AbstractWe prove a fixed point theorem for continuous mappings which satisfy a compression-expansion condition on the boundary of a N-dimensional cell of ℝ

scholarly journals ℤd-actions with prescribed topological and ergodic properties

2011 ◽  
Vol 32 (1) ◽  
pp. 191-209 ◽  
Author(s):  
YURI LIMA
Keyword(s):  
Topological Entropy ◽  
Topological Dynamics ◽  
Ergodic Transformations ◽  
Positive Topological Entropy ◽  
Ergodic Properties ◽  
Uniquely Ergodic

AbstractWe extend constructions of Hahn and Katznelson [On the entropy of uniquely ergodic transformations. Trans. Amer. Math. Soc.126 (1967), 335–360] and Pavlov [Some counterexamples in topological dynamics. Ergod. Th. & Dynam. Sys.28 (2008), 1291–1322] to ℤd-actions on symbolic dynamical spaces with prescribed topological and ergodic properties. More specifically, we describe a method to build ℤd-actions which are (totally) minimal, (totally) strictly ergodic and have positive topological entropy.

Unpredictability in Topological Dynamics

2020 ◽  
pp. 57-79
Author(s):  
Marat Akhmet ◽  
Mehmet Onur Fen ◽  
Ejaily Milad Alejaily
Keyword(s):  
Topological Dynamics

scholarly journals Topological dynamics and the complexity of strong types

2018 ◽  
Vol 228 (2) ◽  
pp. 863-932 ◽  
Author(s):  
Krzysztof Krupiński ◽  
Anand Pillay ◽  
Tomasz Rzepecki
Keyword(s):  
Topological Dynamics

scholarly journals New results on topological dynamics of antitriangular maps

2001 ◽  
Vol 2 (1) ◽  
pp. 51 ◽  
Author(s):  
Francisco Balibrea ◽  
J.S. Cánovas ◽  
A. Linero
Keyword(s):  
Metric Space ◽  
Topological Dynamics ◽  
Compact Metric Space ◽  
Special Analysis ◽  
Continuous Maps

<p>We present some results concerning the topological dynamics of antitriangular maps, F:X<sup>2</sup>→ X<sup>2 </sup>with the formvF(x,y)=(g(y),f(x)), where (X,d) is a compact metric space and f,g : X→ X are continuous maps. We make an special analysis in the case of X = [0,1].</p>

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