arXiv subjects

Mahsa Allahbakhshi

Publications and source records attributed to Mahsa Allahbakhshi.

4 recordsLinked to original sources

arXiv2015

Class-closing factor codes and constant-class-to-one factor codes from shifts of finite type

We define class-closing factor codes from shifts of finite type and show that they are continuing if their images are of finite type. We establish several relations between class-closing factor codes, continuing factor codes and constant-class-to-one factor codes. In particular it is shown that a factor code between irreducible shifts of finite type is constant-class-to-one if and only if it is bi-class-closing, generalizing a result of Nasu.

math.DS↗

arXiv2014

Computing degree and class degree

Let $π$ be a factor code from a one dimensional shift of finite type $X$ onto an irreducible sofic shift $Y$. If $π$ is finite-to-one then the number of preimages of a typical point in $Y$ is an invariant called the degree of $π$. In this paper we present an algorithm to compute this invariant. The generalized notion of the degree when $π$ is not limited to finite-to-one factor codes, is called the class degree of $π$. The class degree of a code is defined to be the number of transition classes over a typical point of $Y$ and is invariant under topological conjugacy. We show that the class degree is computable.

math.DS↗

arXiv2014

Structure of transition classes for factor codes on shifts of finite type

Given a factor code $π$ from a shift of finite type $X$ onto a sofic shift $Y$, the class degree of $π$ is defined to be the minimal number of transition classes over points of $Y$. In this paper we investigate structure of transition classes and present several dynamical properties analogous to the properties of fibers of finite-to-one codes. As a corollary, we show that for an irreducible factor triple there cannot be a transition between two different transition classes over a right transitive point, answering a question raised by Quas.

math.DS↗

arXiv2011

Class Degree and Relative Maximal Entropy

Given a factor code $π$ from a one-dimensional shift of finite type $X$ onto an irreducible sofic shift $Y$, if $π$ is finite-to-one there is an invariant called the degree of $π$ which is defined the number of preimages of a typical point in $Y$. We generalize the notion of the degree to the class degree which is defined for any factor code on a one-dimensional shift of finite type. Given an ergodic measure $ν$ on $Y$, we find an invariant upper bound on the number of ergodic measures on $X$ which project to $ν$ and have maximal entropy among all measures in the fibre $π^{-1}\{ν\}$. We show that this bound and the class degree of the code agree when $ν$ is ergodic and fully supported. One of the main ingredients of the proof is a uniform distribution property for ergodic measures of relative maximal entropy.

math.DS↗