Related papers: Mean Diameter, Regularity and Diam-Mean Equicontin…

Let $G$ be a countable infinite amenable group, $K$ a finite-dimensional compact metrizable space, and $(K^G,\sigma)$ the full $G$-shift on $K^G$. For any $r\in [0,{\rm mdim}(K^G,\sigma))$, we construct a minimal subshift $(X,\sigma)$ of…

Let $\A$ be the operator which assigns to each $m \times n$ matrix-valued function on the unit circle with entries in $H^\infty + C$ its unique superoptimal approximant in the space of bounded analytic $m \times n$ matrix-valued functions…

In this article we give a complete description of the evolution of an area decreasing map $f:M\to N$ induced by its mean curvature in the situation where $M$ and $N$ are complete Riemann surfaces with bounded geometry, $M$ being compact,…

For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.

We characterize amenability of subspaces of $C(S)$, where $S$ is a semitopological semigroup, in terms of fixed point properties of nonexpansive actions. In particular, we give a complete characterization of a semitopological semigroup with…

Consider a quantum cat map $M$ associated to a matrix $A\in\mathop{\mathrm{Sp}}(2n,\mathbb Z)$, which is a common toy model in quantum chaos. We show that the mass of eigenfunctions of $M$ on any nonempty open set in the position-frequency…

In this paper, we introduce the notion of negatively regionally proximal pairs of onto maps which coincides with the set of regionally proximal pair of $f^{-1}$, whenever $f$ is an homeomorphism and we prove the maximal equicontinoues…

Equivariant indices have previously been defined in cases where either the group or the orbit space in question is compact. In this paper, we develop an equivariant index without assuming the group or the orbit space to be compact. This…

Let M be a bounded domain of a Euclidian space with smooth boundary. We relate the Cheeger constant of M and the conductance of a neighborhood graph defined on a random sample from M. By restricting the minimization defining the latter over…

We investigate length decreasing maps $f:M\to N$ between Riemannian manifolds $M$, $N$ of dimensions $m\ge 2$ and $n$, respectively. Assuming that $M$ is compact and $N$ is complete such that…

For meromorphic maps of complex manifolds, ergodic theory and pluripotential theory are closely related. In nice enough situations, dynamically defined Green's functions give rise to invariant currents which intersect to yield measures of…

We show that an $R^d$-topological dynamical system equipped with an invariant ergodic measure has discrete spectrum if and only it is $\mu$-mean equicontinuous (proven for $Z^d$ before). In order to do this we introduce mean equicontinuity…

In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…

We study the local-triviality dimensions of actions on $C^*$-algebras, which are invariants developed for noncommutative Borsuk-Ulam theory. While finiteness of the local-triviality dimensions is known to guarantee freeness of an action, we…

It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…

We call a function $f: X\to Y$ $P$-preserving if, for every subspace $A \subset X$ with property $P$, its image $f(A)$ also has property $P$. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural…

We give a concrete sufficient condition for a simply-connected domain to be the image of the unit disk under a nonexpansive conformal map. This class of domains is also characterized by having sufficiently dense harmonic measure. The…

We find conditions under which two measure preserving actions of two groups on the same space have a common fundamental domain. Our results apply to commuting actions with separate fundamental domains, lattices in groups of polynomial…

The commuting graph of a group G, denoted by Gamma(G), is the simple undirected graph whose vertices are the non-central elements of G and two distinct vertices are adjacent if and only if they commute. Let Z_m be the commutative ring of…

In this article we study minimal equicontinuous actions on Stone spaces, which we call \emph{subodometers}, and do neither assume that the space is metrizable, nor any assumptions on the acting group. We show that the set of eigenvalues is…