Related papers: Topological Dynamics of Closed Subgroups of $S_\in…

This small survey of basic universal constructions related to the actions of topological groups on compacta is centred around a new result --- an intrinsic description of extremely amenable topological groups (i.e., those having a fixed…

In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This enables us to answer positively a question of Bowen and…

We show that for every non-elementary hyperbolic group, an associated topological flow space admits a coding based on a transitive subshift of finite type. Applications include regularity results for Manhattan curves, the uniqueness of…

We propose an entropic geometrical model of crowd behavior dynamics (with dissipative crowd kinematics), using Feynman action--amplitude formalism that operates on three synergetic levels: macro, meso and micro. The intent is to explain the…

In this work, we study the dynamical properties of Krystyna Kuperberg's aperiodic flows on $3$-manifolds. We introduce the notion of a ``zippered lamination'', and with suitable generic hypotheses, show that the unique minimal set for such…

In this expository paper we describe an unifying approach for many known entropies in Mathematics. First we recall the notion of semigroup entropy h_S in the category S of normed semigroups and contractive homomorphisms, recalling also its…

A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this…

The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform…

We consider a smooth closed surface $M$ of fixed genus $\geqslant 2$ with a Riemannian metric $g$ of negative curvature with fixed total area. The second author has shown that the topological entropy of geodesic flow for $g$ is greater than…

In this paper, we extend a Ma\~n\'e's famous result on expansive homeomorphisms, originally presented in [17], to the setting of flows. Specifically, we provide a complete characterization of minimal expansive flows without fixed points on…

We investigate $\mathbb{R}^n$ as the additive group with the Euclidean topology to give a description of $S(\mathbb{R}^n)$, the phase space of the universal ambit of $\mathbb{R}^n$ and $M(\mathbb{R}^n)$, the phase space of the universal…

A topological group $G$ is extremely amenable if every continuous action of $G$ on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of…

In this work, we introduce a natural class of chaotic flows on non-compact manifolds, called H-flows, which includes geodesic flows on non-compact manifolds with pinched negative curvature. We show that, under the additional assumption,…

Let $T$ be a theory which is t-minimal, meaning that with respect to some definable topology, a unary definable set $D \subseteq M$ has non-empty interior iff it is infinite. If $K$ is a definable field in $T$, then $K$ is finite or "large"…

Let $\mathcal{F} $ be a pointwise almost periodic decomposition of a compact metrizable space $X$. Then $\mathcal{F} $ is $R$-closed if and only if $\hat{\mathcal{F}} $ is usc. Moreover, if there is a finite index normal subgroup $H$ of an…

We show that on a smooth Hermitian minimal model of general type the Chern-Ricci flow converges to a closed positive current on M. Moreover, the flow converges smoothly to a Kahler-Einstein metric on compact sets away from the null locus of…

In this article we study geodesic flows on closed Riemannian manifolds without conjugate points and divergence property of geodesic rays. If the fundamental group is Gromov hyperbolic and residually finite we prove, under appropriate…

We prove that, whenever $G$ is a Polish group with metrizable universal minimal flow $M(G)$, there exists a comeagre orbit in $M(G)$. It then follows that there exists an extremely amenable, closed, coprecompact $G^*$ of $G$ such that $M(G)…

Let $M=X/\Gamma$ be a geometrically finite negatively curved manifold with fundamental group $\Gamma$ acting on $X$ by isometries. The purpose of this paper is to study the mixing property of the geodesic flow on $T^1M$, the asymptotic…

We characterize Markov lattice semigroups induced by measurable semiflows on probability spaces by properties of their generators. In addition we construct topological models on compact spaces for such semigroups.