Related papers: Flows with minimal subdynamics

Let $\Gamma$ be a non-elementary relatively hyperbolic group with a finite generating set. Consider a finitely supported admissible and symmetric probability measure $\mu$ on $\Gamma$ and a probability measure $\nu$ on $\mathbb{N}$ with…

Let $\Sigma$ be a smooth Riemannian manifold, $\Gamma \subset \Sigma$ a smooth closed oriented submanifold of codimension higher than $2$ and $T$ an integral area-minimizing current in $\Sigma$ which bounds $\Gamma$. We prove that the set…

Let $\Gamma$ be a compact Polish group of finite topological dimension. For a countably infinite subset $S\subseteq \Gamma$, a domatic $\aleph_0$-partition (for its Schreier graph on $\Gamma$) is a partial function…

We study the renormalization group flow in a class of scalar-tensor theories involving at most two derivatives of the fields. We show in general that minimal coupling is self consistent, in the sense that when the scalar self couplings are…

Let $X$ be the $2$-sphere $\mathbb S^2$ or the real projective plane $\mathbb {RP}^2$. We show that if $\Gamma$ is a finitely generated group acting minimally and distally on $X$, then $\Gamma$ contains a nonabelian free subgroup.

Let $n, m\ge 2$. Let $\Gamma<\text{SO}^\circ(n+1,1)$ be a Zariski dense convex cocompact subgroup and $\Lambda\subset\mathbb{S}^n$ be its limit set. Let $\rho : \Gamma \to \text{SO}^\circ(m+1,1)$ be a Zariski dense convex cocompact faithful…

A theorem of Gao, Jackson and Seward, originally conjectured to be false by Glasner and Uspenskij, asserts that every countable group admits a $2$-coloring. A direct consequence of this result is that every countable group has a strongly…

Let $\boldsymbol{B}_{\omega}^{\mathscr{F}}$ be the bicyclic semigroup extension for the family $\mathscr{F}$ of ${\omega}$-closed subsets of $\omega$ which is introduced in \cite{Gutik-Mykhalenych=2020}. We study topologizations of the…

Let $(T,X)$ with phase mapping $(t,x)\mapsto tx$ be a semiflow on a compact $\textrm{T}_2$-space $X$ with phase semigroup $T$ such that $tX=X$ for each $t$ of $T$. An $x\in X$ is called an \textit{a.a. point} if $t_nx\to y, x_n^\prime\to…

We say that a subset $X$ quasi-isometrically boundedly generates a finitely generated group $\Gamma$ if each element $\gamma$ of a finite-index subgroup of $\Gamma$ can be written as a product $\gamma = x_1 x_2 \cdots x_r$ of a bounded…

In the first part of this paper we prove that the flow associated to a dispersive Burgers equation with a non local term of the form $|D|^{\alpha-1} \partial_x u$, $\alpha \in [1,+\infty[$ is Lipschitz from bounded sets of…

Let $\Gamma$ be a discrete group acting freely via homeomorphisms on the compact Hausdorff space $X$ and let $C(X) \rtimes_\eta \Gamma$ be the completion of the convolution algebra $C_c(\Gamma,C(X))$ with respect to a $C^*$-norm $\eta$. A…

We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense.…

We consider a free group extension of a subshift of finite type $\sigma:\Sigma\rightarrow\Sigma$, and consider three sets of points in $\Sigma$ to which the corresponding trajectories on the free group escape to a given point in the Gromov…

We show that the Heisenberg type group $H_X=(\Bbb{Z}_2 \oplus V) \leftthreetimes V^{\ast}$, with the discrete Boolean group $V:=C(X,\Z_2)$, canonically defined by any Stone space $X$, is always minimal. That is, $H_X$ does not admit any…

Let $G$ be a Lie group, $\Gamma\subset G$ a discrete subgroup, $X=G/\Gamma$, and $f$ an affine map from $X$ to itself. We give conditions on a submanifold $Z$ of $X$ guaranteeing that the set of points $x\in X$ with $f$-trajectories…

We prove a modified version for a conjecture of Weiss from 2004. Let $G$ be a semisimple real algebraic group defined over $\mathbb{Q}$, $\Gamma$ be an arithmetic subgroup of $G$. A trajectory in $G/\Gamma$ is divergent if eventually it…

We study universal minimal flows of the homeomorphism groups of generalized Wa\.zewski dendrites $W_P$, $P\subset\{3,4,\ldots,\omega\}$. If $P$ is finite, we prove that the universal minimal flow of of the homeomorphism group $H(W_P)$ is…

Let $D$ be a regular strictly convex bounded domain of $\mathbb{R}^3$, and consider a regular Jordan curve $\Gamma \subset \partial D$. Then, for each $\epsilon>0$, we obtain the existence of a complete proper minimal immersion…

We study the interplay between the diagonal flow on, and the topology of, a stratum component of a space of rooted quadratic differentials. We prove that the flow group -- the subgroup of the fundamental group generated by almost-flow loops…