Related papers: Gap distributions and homogeneous dynamics

We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that…

We show that Lagrangian measurements in active turbulence bear imprints of turbulent and anomalous streaky hydrodynamics leading to a self-selection of persistent trajectories - Levy walks - over diffusive ones. This emergent dynamical…

We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…

Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…

This is an earlier, but more general, version of "An L^1 Ergodic Theorem for Sparse Random Subsequences". We prove an L^1 ergodic theorem for averages defined by independent random selector variables, in a setting of general…

We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\operatorname{SL}_2(\mathbb R)$ in arithmetic quotients of $\operatorname{SL}_2(\mathbb C)$ and $\operatorname{SL}_2(\mathbb…

Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…

We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show, with some examples, that representation theory of semigroups is related to usual constructions in…

We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces $\mathcal{H}(2)$. Especially, we obtain effective density theorems on $\mathcal{H}(2)$ for orbits of the upper triangular subgroup $P$ of…

In the first part of the paper we show that the ring of global sections of arithmetic differential operators on the formal projective line over Zp is isomorphic to the analytic distribution algebra of the 'wide open' congruence subgroup of…

A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…

We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents.…

We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…

We develop a Galois theory for difference ring extensions, inspired by Magid's separable Galois theory for ring extensions and by Janelidze's categorical Galois theory. Our difference Galois theorem states that the category of difference…

We establish the spectral gap property for dense subgroups generated by algebraic elements in any compact simple Lie group, generalizing earlier results of Bourgain and Gamburd for unitary groups.

We define polygonal dynamics as a family of dynamical systems acting on points in projective spaces. The most famous example is the pentagram map. Similar collapsing phenomena seem to occur in most of these systems. We prove it in some…

The existence of a strong spectral gap for quotients $\Gamma\bs G$ of noncompact connected semisimple Lie groups is crucial in many applications. For congruence lattices there are uniform and very good bounds for the spectral gap coming…

We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…