Related papers: Totally Rank One Interval Exchange Transformations
We study influence of ordinal transformations on results of queries in rank-aware databases which derive their operations with ranked relations from totally ordered structures of scores with infima acting as aggregation functions. We…
We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
Let E denote the group of all interval exchange transformations on [0,1). Given a suitable topological group structure on E, it is possible to classify all one-parameter interval exchange actions (continuous homomorphisms from R to E). In…
The Arnoux-Rauzy systems are defined in \cite{ar}, both as symbolic systems on three letters and exchanges of six intervals on the circle. In connection with a conjecture of S.P. Novikov, we investigate the dynamical properties of the…
In this paper some sufficient conditions are given for when two bounded rank-one transformations are isomorphic or disjoint. For commensurate, canonically bounded rank-one transformations, isomorphism and disjointness are completely…
The conservative sequence of a set $A$ under a transformation $T$ is the set of all $n \in \mathbb{Z}$ such that $T^n A \cap A \not = \varnothing$. By studying these sequences, we prove that given any countable collection of nonsingular…
For positive $q\neq1$, the $q$-exchangeability of an infinite random word is introduced as quasi-invariance under permutations of letters, with a special cocycle which accounts for inversions in the word. This framework allows us to extend…
We consider piecewise monotone maps, we show that an ergodic measure for which the map is invertible almost everywhere can not be mixing. It follows that every ergodic measure for an interval translation mapping is not mixing. We also show…
We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the…
We study discontinuous interval maps generated by the action of erasing block substitutions on the binary expansion. After establishing some general properties of these maps, we categorize erasing block substitutions in a hierarchy of…
We characterize Leavitt path algebras which are exchange rings in terms of intrinsic properties of the graph and show that the values of the stable rank for these algebras are 1, 2 or $\infty$. Concrete criteria in terms of properties of…
For almost all interval exchange maps T_0, with combinatorics of genus g>=2, we construct affine interval exchange maps T which are semi-conjugate to T_0 and have a wandering interval.
We study the rich behavior of ergodicity and conservativity of Cartesian products of infinite measure preserving transformations. A class of transformations is constructed such that for any subset $R\subset \mathbb Q\cap (0,1)$ there exists…
Maps $f,g\colon I\to I$ are called strongly commuting if $f\circ g^{-1}=g^{-1}\circ f$. We show that strongly commuting, piecewise monotone maps $f,g$ can be decomposed into a finite number of invariant intervals (or period 2 intervals) on…
For $i = 0, 1, 2, \dots, k$, let $\mu_i$ be a Borel probability measure on $[0,1]$ which is equivalent to Lebesgue measure $\lambda$ and let $T_i:[0,1] \rightarrow [0,1]$ be $\mu_i$-preserving ergodic transformations. We say that…
We study linear recurrence and weak mixing of a two-parameter family of interval translation maps $T_{\alpha,\beta}$ for the subset of parameter space where $T_{\alpha,\beta}$ has a Cantor attractor. For this class, there is a procedure…
We give a description of a weakly continuous rank preserving map on a reflexive algebra on complex Hilbert space with commutative completely distributive subspace lattice. We show that the implementation of a rank preserving map can be…
We present the first rigorous quantitative analysis of once-reinforced random walks (ORRW) on general graphs, based on a novel change of measure formula.~This enables us to prove large deviations estimates for the range of the walk to have…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…