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We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is…
Context. Among the main effects that the Milky Way exerts in binary systems, the Galactic tide is the only one that is not probabilistic and can be deduced from a potential. Therefore, it is possible to perform an analysis of the global…
We study equatorial closed orbits in a popular black bounce model to see if the internal structure of these objects could lead to peculiar observable features. Paralleling the analysis of the Schwarzschild and Kerr metrics, we show that in…
Inspired by the work of Pujals and Sambarino on dominated splitting, we present billiards with a modified reflection law which constitute simple examples of dynamical systems with limit sets with dominated splitting and where the dynamics…
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive…
We analyze time crystal effects in a finite system of bosons which form a bright soliton clump on the Aharonov-Bohm ring. In the large particle number limit, $N\rightarrow\infty$, this setup corresponds to the Wilczek model, where it is…
Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I…
A necklace is an equivalence class of words of length $n$ over an alphabet under the cyclic shift (rotation) operation. As a classical object, there have been many algorithmic results for key operations on necklaces, including counting,…
In this paper we investigate the unbounded Kasparov product between a differentiable module and an unbounded cycle of a very general kind that includes all unbounded Kasparov modules and hence also all spectral triples. Our assumptions on…
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…
We study the classical dynamics of the universe undergoing a transition from contraction to expansion through a big bang singularity. The dynamics is described by a system of differential equations for a set of physical quantities, such as…
By proving a local limit theorem for higher-order transitions, we determine the time required for necklace chains to be close to stationarity. Because necklace chains, built by arranging identical smaller chains around a directed cycle, are…
We apply periodic orbit theory to a quantum billiard on a torus with a variable number N of small circular scatterers distributed randomly. Provided these scatterers are much smaller than the wave length they may be regarded as sources of…
The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, $\E$, such that the question of membership in this orbit is $\Sigma^1_1$-complete. This result and proof have a number of nice corollaries: the…
We consider heavy-tailed observables maximised on a dynamically defined Cantor set and prove convergence of the associated point processes as well as functional limit theorems. The Cantor structure, and its connection to the dynamics,…
We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…
We consider a system of four one-dimensional inelastic hard spheres evolving on the real line $\mathbb{R}$, and colliding according to a scattering law characterized by a fixed restitution coefficient $r$. We study the possible orders of…
The individual component spins of binary black holes (BBHs) are difficult to resolve using gravitational-wave observations but carry key signatures of the processes shaping their formation and evolution. Recent analyses have found…
We revisit the r\^{o}le of discreteness and chaos in the dynamics of self-gravitating systems by means of $N$-body simulations with active and frozen potentials, starting from spherically symmetric stationary states and considering the…
The richness of dynamical behavior exhibited by the rotational states of various solar system objects has driven significant advances in the theoretical understanding of their evolutionary histories. An important factor that determines…