scholarly journals Topological and almost Borel universality for systems with the weak specification property

2019 ◽  
Vol 40 (8) ◽  
pp. 2098-2115 ◽  
Author(s):  
DAVID BURGUET
Keyword(s):  
Dynamical Systems ◽  
Specification Property ◽  
Lower Entropy ◽  
Topological Dynamical Systems

We show that systems with some specification properties are topologically or almost Borel universal, in the sense that any aperiodic subshift with lower entropy may be topologically or almost Borel embedded. This improves, with elementary tools, previous results of Quas and Soo [Ergodic universality of some topological dynamical systems. Trans. Amer. Math. Soc.368 (2016), 4137–4170].

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

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

On the dynamics of the Tent function - Phase diagrams

2016 ◽  
Vol 7 (4) ◽  
pp. 261
Author(s):  
Prince Amponsah Kwabi ◽  
William Obeng Denteh ◽  
Richard Kena Boadi
Keyword(s):  
Dynamical Systems ◽  
Phase Diagrams ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Topological Dynamical System ◽  
Topological Transitivity ◽  
Tent Map ◽  
One Dimensional ◽  
Definition Of ◽  
Topological Dynamical Systems

This paper focuses on the study of a one-dimensional topological dynamical system, the tent function. We give a good background to the theory of dynamical systems while establishing the important asymptotic properties of topological dynamical systems that distinguishes it from other fields by way of an example - the tent function. A precise definition of the tent function is given and iterates are clearly shown using the phase diagrams. By this same method, chaos in the tent map is shown as iterates become higher. We also show that the tent map has infinitely many chaotic orbits and also express some important features of chaos such as topological transitivity, boundedness and sensitivity to change in initial conditions from a topological viewpoint.

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