On the algebraic properties of the automorphism groups of countable-state Markov shifts

2006 ◽  
Vol 26 (02) ◽  
pp. 551 ◽  
Author(s):  
MICHAEL SCHRAUDNER
Keyword(s):  
Automorphism Groups ◽  
Markov Shifts ◽  
Algebraic Properties ◽  
Countable State

Topological Boundaries for Countable State Markov Shifts

1995 ◽  
Vol s3-70 (3) ◽  
pp. 625-643 ◽  
Author(s):  
Doris Fiebig ◽  
Ulf-Rainer Fiebig
Keyword(s):  
Markov Shifts ◽  
Countable State

Pressure and equilibrium states for countable state markov shifts

2002 ◽  
Vol 131 (1) ◽  
pp. 221-257 ◽  
Author(s):  
Doris Fiebig ◽  
Ulf-Rainer Fiebig ◽  
Michiko Yuri
Keyword(s):  
Equilibrium States ◽  
Markov Shifts ◽  
Countable State

scholarly journals Induced topological pressure for countable state Markov shifts

2014 ◽  
Vol 14 (02) ◽  
pp. 1350016 ◽  
Author(s):  
Johannes Jaerisch ◽  
Marc Kesseböhmer ◽  
Sanaz Lamei
Keyword(s):  
Large Class ◽  
Group Structure ◽  
Topological Pressure ◽  
Hölder Continuous ◽  
Dynamical Group ◽  
Height Functions ◽  
Markov Shifts ◽  
Countable State ◽  
Set Up ◽  
Definition Of

We generalise Savchenko's definition of topological entropy for special flows over countable Markov shifts by considering the corresponding notion of topological pressure. For a large class of Hölder continuous height functions not necessarily bounded away from zero, this pressure can be expressed by our new notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words, and we are able to set up a variational principle in this context. Investigating the dependence of induced pressure on the subset of words, we give interesting new results connecting the Gurevič and the classical pressure with exhaustion principles for a large class of Markov shifts. In this context we consider dynamical group extensions to demonstrate that our new approach provides a useful tool to characterise amenability of the underlying group structure.

scholarly journals Compact factors of countable state Markov shifts

2002 ◽  
Vol 270 (1-2) ◽  
pp. 935-946 ◽  
Author(s):  
Doris Fiebig ◽  
Ulf-Rainer Fiebig
Keyword(s):  
Markov Shifts ◽  
Countable State

Canonical compactifications for Markov shifts

2012 ◽  
Vol 33 (2) ◽  
pp. 441-454 ◽  
Author(s):  
DORIS FIEBIG
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Complete Characterization ◽  
Markov Shift ◽  
Locally Compact ◽  
Markov Shifts ◽  
Countable State ◽  
State Mixing ◽  
The Given

AbstractWe give a complete characterization of the compact metric dynamical systems that appear as boundaries of the canonical compactification of a locally compact countable state mixing Markov shift. Consider such a compact metric dynamical system. Then there is a pair of non-conjugate Markov shifts with conjugate canonical compactifications, one of which has the given compact system as canonical boundary.

scholarly journals On the automorphism groups of multidimensional shifts of finite type

2009 ◽  
Vol 30 (3) ◽  
pp. 809-840 ◽  
Author(s):  
MICHAEL HOCHMAN
Keyword(s):  
Automorphism Group ◽  
Finite Type ◽  
Infinite Order ◽  
Automorphism Groups ◽  
Positive Entropy ◽  
Minimal Points ◽  
Algebraic Properties ◽  
Full Shift ◽  
Shift Action ◽  
The One

AbstractWe investigate algebraic properties of the automorphism group of multidimensional shifts of finite type (SFTs). We show that positive entropy implies that the automorphism group contains every finite group and, together with transitivity, implies that the center of the automorphism group is trivial (i.e. consists only of the shift action). We also show that positive entropy and dense minimal points (in particular, dense periodic points) imply that the automorphism group of X contains a copy of the automorphism group of the one-dimensional full shift, and hence contains non-trivial elements of infinite order. On the other hand we construct a mixing, positive-entropy SFT whose automorphism group is, modulo the shift action, a union of finite groups.

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