arXiv subjects
Publications and source records attributed to Jesús Antonio Álvarez López.
We present a definition of chaotic Delone set, and establish the genericity of chaos in the space of $(ε,δ)$-Delone sets for $ε\geq δ$. We also present a hyperbolic analogue of the cut-and-project method that naturally produces examples of chaotic Delone sets.
Let $X$ be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring $ϕ\colon X\to\{0,1\}$ and some $R\in\mathbb{N}$ such that every automorphism $f$ preserving $ϕ$ is $R$-close to the identity map; this can be seen as a coarse geometric version of symmetry breaking. We also prove that the infinite motion conjecture is true for graphs where at least one vertex stabilizer $S_x$ satisfies the following condition: for every non-identity automorphism $f\in S_x$, there is a sequence $x_n$ such that $\lim d(x_n,f(x_n))=\infty$.
The purpose of this article is to compute the expected first exit times of Brownian motion from a variety of domains in the Euclidean plane and in the hyperbolic plane.