Related papers: Simultaneous dense and nondense orbits for noncomm…

Let $G/\Gamma$ be the quotient of a semisimple Lie group by an arithmetic lattice. We show that for reductive subgroups $H$ of $G$ that is large enough, the orbits of $H$ on $G/\Gamma$ intersect nontrivially with a fixed compact set. As a…

Let $\nu$ be a probability measure that is ergodic under the endomorphism $(\times p, \times p)$ of the torus $\mathbb{T}^2$, such that $\dim \pi \mu < \dim \mu$ for some non-principal projection $\pi$. We show that, if both $m\neq n$ are…

We consider infinite sequences of superstable orbits (cascades) generated by systematic substitutions of letters in the symbolic dynamics of one-dimensional nonlinear systems in the logistic map universality class. We identify the…

In [6], Geroch, Kronheimer and Penrose introduced a way to attach ideal points to a spacetime M , defining the causal completion of M. They established that this is a topological space which is Hausdorff when M is globally hyperbolic. In…

Given an integer nonsingular $n\times n$ matrix $M$ and a point $y \in \mathbb{R}^n/\mathbb{Z}^n$, consider the set $\tilde E(M,y)$ of vectors $x\in \mathbb{R}^n$ such that $y$ is not a limit point of the sequence $\{M^k x \mod…

We study the superconducting state of multi-orbital spin-orbit coupled systems in the presence of an orbitally driven inversion asymmetry assuming that the inter-orbital attraction is the dominant pairing channel. Although the inversion…

In this paper, we assume that all isoparametric submanifolds have flat section. The main purpose of this paper is to prove that, if a full irreducible complete isoparametric submanifold of codimension greater than one in a symmetric space…

Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle $\mathrm{PSL}_2(\mathbb{Z})\backslash\mathrm{PSL}_2(\mathbb{R})$. The complement of any finite number of orbits is a…

We construct pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume. Topologically these orbifolds are mapping tori of pseudo-Anosov maps of the surface of genus 2, with singular locus a fibred (hyperbolic)…

This paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets of $\mathbb{R}^{2n}$, as well as dimension of intersections of sets with isotropic planes. It is shown that if $A$ and $B$ are Borel subsets…

In this paper we consider expansive homeomorphisms of compact spaces with a hyperbolic metric presenting a self-similar behavior on stable and unstable sets. Several application are given related to Hausdorff dimension, entropy,…

Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…

In this paper, we study the Hausdorff dimension of the Floyd and Bowditch boundaries of a relatively hyperbolic group, and show that for the Floyd metric and shortcut metrics respectively, they are are both equal to a constant times the…

Any one-cusped hyperbolic manifold M with an unknotting tunnel tau is obtained by Dehn filling a cusp of a two-cusped hyperbolic manifold. In the case where M is obtained by "generic" Dehn filling, we prove that tau is isotopic to a…

A biperiodic alternating link has an alternating quotient link in the thickened torus. In this paper, we focus on semi-regular links, a class of biperiodic alternating links whose hyperbolic structure can be immediately determined from a…

Suppose that a group $G$ acts non-elementarily on a hyperbolic space $S$ and does not fix any point of $\partial S$. A subgroup $H\le G$ is said to be geometrically dense in $G$ if the limit sets of $H$ and $G$ coincide and $H$ does not fix…

Semi-classically equivalent field theories are related by a quasi-isomorphism between their underlying $L_\infty$-algebras, but such a quasi-isomorphism is not necessarily a homotopy transfer. We demonstrate that all quasi-isomorphisms can…

In this paper, we study the weighted $n$-dimensional badly approximable points on manifolds. Given a $C^n$ differentiable non-degenerate submanifold $\mathcal{U} \subset \mathbb{R}^n$, we will show that any countable intersection of the…

If H is a flat group of automorphisms of finite rank n of a totally disconnected, locally compact group G, then each orbit of H in the metric space B(G) of compact, open subgroups of G is quasi-isometric to n-dimensional euclidean space. In…

Ivansic proved that there is a link $L$ of five tori in $S^4$ with hyperbolic complement. We describe $L$ explicitly with pictures, study its properties, and discover that $L$ is in many aspects similar to the Borromean rings in $S^3$. In…