Subshifts of quasi-finite type
By Jérôme Buzzi. 2003
58 citations recorded by the source corpus.
We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems, e.g., piecewise monotonic maps of the interval with positive entropy. Yet many properties remain: existence of finitely many ergodic invariant probabilities of maximum entropy; lots of periodic points; meromorphic extension of the Artin-Mazur zeta function.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8fba2e3ee4207d7e08dabe18eea93509e76dc16f
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In Computational Theory and Mathematics
In Mathematical Physics
- Jérôme Buzzi
- S. Crovisier
- O. Sarig
- Mike Boyle
- Ricardo Gómez
- Marcelo Viana
- P. Varandas
- Dominik Kwietniak
Citations in the corpus
- Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps (2008, background): “An important notion of entropy-expansiveness was introduced by Buzzi [12], which influenced [14,38] among other papers.”
- Measures of maximal entropy for surface diffeomorphisms (2018, background): “[16, 41]), and related symbolic systems [27, 88, 29, 39, 73].”
- A PANORAMA OF SPECIFICATION-LIKE PROPERTIES AND THEIR CONSEQUENCES (2015, background): “Buzzi [17] investigated a class of shifts which arose in symbolic coding of several classes of non-uniformly hyperbolic dynamical systems such as entropy-expanding maps.”
- Almost isomorphism for countable state Markov shifts (2004, methodology): “We will not define the class of subshifts of quasi finite type [ 10 ]; this is a useful class of finite state subshifts which contains the class of subshifts of finite type, but is much larger (for example, every finite positive entropy is achieved by a subshift of quasi finite type).”