Countable State Markov Shifts

1998 ◽  
pp. 195-240 ◽  
Author(s):  
Bruce P. Kitchens
Keyword(s):  
Markov Shifts ◽  
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 Manhattan curves for hyperbolic surfaces with cusps

2018 ◽  
Vol 40 (7) ◽  
pp. 1843-1874 ◽  
Author(s):  
LIEN-YUNG KAO
Keyword(s):  
Riemann Surfaces ◽  
Thermodynamic Formalism ◽  
Compact Surface ◽  
Hyperbolic Surfaces ◽  
Rigidity Results ◽  
Markov Shifts ◽  
Countable State ◽  
Geometric Rigidity ◽  
Convex Cocompact ◽  
Rank 2

In this paper, we study an interesting curve, the so-called Manhattan curve, associated with a pair of boundary-preserving Fuchsian representations of a (non-compact) surface; in particular, representations corresponding to Riemann surfaces with cusps. Using thermodynamic formalism (for countable state Markov shifts), we prove the analyticity of the Manhattan curve. Moreover, we derive several dynamical and geometric rigidity results, which generalize results of Burger [Intersection, the Manhattan curve, and Patterson–Sullivan theory in rank 2. Int. Math. Res. Not.1993(7) (1993), 217–225] and Sharp [The Manhattan curve and the correlation of length spectra on hyperbolic surfaces. Math. Z.228(4) (1998), 745–750] for convex cocompact Fuchsian representations.

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