Related papers: Dendrites and measures with discrete spectrum

In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply…

We proved recently that a measure on R, whose support and spectrum are both uniformly discrete sets, must have a periodic structure. Here we show that this is not the case if the support and the spectrum are just discrete closed sets.

We prove that for certain actions of a discrete countable residually finite amenable group acting on a compact metric space with specification property, periodic measures are dense in the set of invariant measures.

We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.

In this paper we investigate the problems related to measures with a natural spectrum (equal to the closure of the set of the values of the Fourier-Stieltjes transform). Since it is known that the set of all such measures does not have a…

We study the structure of invariant measures for continuous automorphisms of compact metrizable abelian groups satisfying the descending chain condition. We show that the finitely supported invariant measures are weak-* dense in the space…

Delone sets of finite local complexity in Euclidean space are investigated. We show that such a set has patch counting and topological entropy 0 if it has uniform cluster frequencies and is pure point diffractive. We also note that the…

We study relations between transitivity, mixing and periodic points on dendrites. We prove that when there is a point with dense orbit which is not an endpoint, then periodic points are dense and there is a terminal periodic decomposition…

For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure.…

In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework.…

In spaces of metrics, we investigate topological distributions of the doubling property, the uniform disconnectedness, and the uniform perfectness, which are the quasi-symmetrically invariant properties appearing in the David--Semmes…

It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular,…

This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the…

The discrete spectrum of complex banded matrices which are compact perturbations of the standard banded matrix of order $p$ is under consideration. The rate of stabilization for the matrix entries sharp in the sense of order which provides…

We prove that among the set of smooth diffeomorphisms there exists a $C^1$-open and dense subset of data such that either the Lagrange spectrum is finite and the dynamics is a Morse-Smale diffeomorphism or the Lagrange spectrum has positive…

Any ergodic measure of a smooth map on a compact manifold has a multifractal spectrum with one point - the dimension of the measure itself - at the diagonal. We will construct examples where this fails in the most drastic way for invariant…

We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire,…

We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…

A topological space is iso-dense if it has a dense set of isolated points. A topological space is scattered if each of its non-empty subspaces has an isolated point. In $\mathbf{ZF}$, in the absence of the axiom of choice, basic properties…

We present a new approach to singularity confinement which makes it an efficient and reliable discrete integrability detector. Our method is based on the full-deautonomisation procedure, which consists in analysing non-autonomous extensions…