Dendritations of surfaces

2017 ◽  
Vol 38 (8) ◽  
pp. 2860-2912 ◽  
Author(s):  
ALFONSO ARTIGUE
Keyword(s):  
Dynamical Systems ◽  
Metric Spaces ◽  
Upper Semicontinuous ◽  
Topological Dynamical Systems ◽  
Stable And Unstable Sets ◽  
Foliated Manifolds

In this paper we develop a generalization of foliated manifolds in the context of metric spaces. In particular we study dendritations of surfaces that are defined as maximal atlases of compatible upper semicontinuous local decompositions into dendrites. Applications are given in modeling stable and unstable sets of topological dynamical systems. For this purpose new forms of expansivity are defined.

scholarly journals Characteristic exponents of dynamical systems in metric spaces

1983 ◽  
Vol 3 (1) ◽  
pp. 119-127 ◽  
Author(s):  
Yuri Kifer
Keyword(s):  
Dynamical Systems ◽  
Metric Spaces ◽  
Invariant Sets ◽  
Characteristic Exponents ◽  
Smooth Case

AbstractWe introduce for dynamical systems in metric spaces some numbers which in the case of smooth dynamical systems turn out to be the maximal and the minimal characteristic exponents. These numbers have some properties similar to the smooth case. Analogous quantities are defined also for invariant sets.

scholarly journals Q-entropy for general topological dynamical systems

2019 ◽  
Vol 39 (4) ◽  
pp. 2059-2075 ◽  
Author(s):  
Yun Zhao ◽  
◽  
Wen-Chiao Cheng ◽  
Chih-Chang Ho ◽  
◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Topological Dynamical Systems

scholarly journals Best Proximity Pairs for Upper Semicontinuous Set-Valued Maps in Hyperconvex Metric Spaces

2008 ◽  
Vol 2008 (1) ◽  
pp. 648985 ◽  
Author(s):  
A Amini-Harandi ◽  
AP Farajzadeh ◽  
D O'Regan ◽  
RP Agarwal
Keyword(s):  
Metric Spaces ◽  
Upper Semicontinuous

scholarly journals Strong Li–Yorke Chaos for Time-Varying Discrete Dynamical Systems with A-Coupled-Expansion

2015 ◽  
Vol 25 (13) ◽  
pp. 1550186 ◽  
Author(s):  
Hua Shao ◽  
Yuming Shi ◽  
Hao Zhu
Keyword(s):  
Dynamical Systems ◽  
Metric Spaces ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Strong Sense ◽  
Time Varying ◽  
Transition Matrices ◽  
Complete Metric Spaces ◽  
Compact Subsets

This paper is concerned with strong Li–Yorke chaos induced by [Formula: see text]-coupled-expansion for time-varying (i.e. nonautonomous) discrete systems in metric spaces. Some criteria of chaos in the strong sense of Li–Yorke are established via strict coupled-expansions for irreducible transition matrices in bounded and closed subsets of complete metric spaces and in compact subsets of metric spaces, respectively, where their conditions are weaker than those in the existing literature. One example is provided for illustration.

Almost topological dynamical systems

1979 ◽  
Vol 34 (1-2) ◽  
pp. 139-160 ◽  
Author(s):  
Manfred Denker ◽  
Michael Keane
Keyword(s):  
Dynamical Systems ◽  
Topological Dynamical Systems
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