Related papers: Infinite Interval Exchange Transformations from Sh…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
In this paper, we study a family of finitely generated elementary amenable iet-groups. These groups are generated by finitely many rationals iets and rotations. For them, we state criteria for not virtual nilpotency or solvability, and we…
We find necessary and sufficient conditions for a dynamical system to be topologically conjugate to any given substitution minimal system, thus extending the results in [CKL] for the Morse and Toeplitz substitutions.
We survey the connections between entropy, chaos, and independence in topological dynamics. We present extensions of two classical results placing the following notions in the context of symbolic dynamics: 1. Equivalence of positive entropy…
For any $\lambda>2$, we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor $\lambda$. In particular, we obtain the first class of examples of substitutive systems with…
We show that strongly positively recurrent Markov shifts (in particular shifts of finite type) are classified up to Borel conjugacy by their entropy, period and their numbers of periodic points.
We study zero-temperature XX chains and transverse Ising chains and join an initially separate finite piece on one or on both sides to an infinite remainder. In both critical and non-critical systems we find a typical increase of the…
We show that if $G$ is a a countable amenable group with the comparison property, and $X$ is a strongly irreducible $G$-shift satisfying certain aperiodicity conditions, then $X$ factors onto the full $G$-shift over $N$ symbols, so long as…
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
In this paper the authors find examples of translation surfaces that have infinitely generated Veech groups, satisfy the topological dichotomy property that for every direction either the flow in that direction is completely periodic or…
We introduce the mean topological dimension for random bundle transformations, and show that continuous bundle random dynamical systems with finite topological entropy, or the small boundary property have zero mean topological dimensions.
We give a "limit-free formula" simplifying the computation of the topological entropy for topological automorphisms of totally disconnected locally compact groups. This result allows us to extend several basic properties of the topological…
In this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a…
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
We prove that skew products with the cocycle given by the function $f(x)=a(x-1/2)$ with $a\neq 0$ are ergodic for every ergodic symmetric IET in the base, thus giving the full characterization of ergodic extensions in this family. Moreover,…
We examine energy and particle exchange between finite-sized quantum systems and find a new form of nonequilibrium states. The exchange rate undergoes stepwise evolution in time, and its magnitude and sign dramatically change according to…
For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak-$*$ topology has infinite topological mean dimension. We also estimate the rate of…
We show the equivalence of two possible definitions of a rotational interval exchange transformation: by the first one, it is a first return map for a circle rotation onto a union of finite number of circle arcs, and by the second one, it…
Positive topological entropy and distributional chaos are characterized for hereditary shifts. A hereditary shift has positive topological entropy if and only if it is DC2-chaotic (or equivalently, DC3-chaotic) if and only if it is not…
We consider word complexity and topological entropy for random substitution subshifts. In contrast to previous work, we do not assume that the underlying random substitution is compatible. We show that the subshift of a primitive random…