Related papers: Intermittency route to chaos for the nuclear billi…
A comprehensive study of periodic trajectories of billiards within ellipsoids in $d$-dimensional Euclidean space is presented. The novelty of the approach is based on a relationship established between periodic billiard trajectories and…
The coupled electron-nuclear spin system in an InGaAs semiconductor as testbed of nonlinear dynamics can develop auto-oscillations, resembling time-crystalline behavior, when continuously excited by a circularly polarized laser. We expose…
We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. These pinball billiards interpolate between a one-dimensional…
We consider chaotic dynamics of a system of two coupled ring resonators with a linear gain and a nonlinear absorption. Such a structure can be implemented in various settings including microresonator nanostructures, polariton condensates,…
We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and against each other. In the one-particle case,…
We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with…
A "drivebelt" stadium billiard with boundary consisting of circular arcs of differing radius connected by their common tangents shares many properties with the conventional "straight" stadium, including hyperbolicity and mixing, as well as…
Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one…
Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…
We present first measurements on a superconducting three-dimensional, partly chaotic microwave billiard shaped like a small deformed cup. We analyze the statistical properties of the measured spectrum in terms of several methods originally…
We consider classical billiards in plane, connected, but not necessarily bounded domains. The charged billiard ball is immersed in a homogeneous, stationary magnetic field perpendicular to the plane. The part of dynamics which is not…
We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees, and it is classically chaotic. The billiard exhibits only…
We introduce the spherical wedge billiard, a dynamical system consisting of a particle moving along a geodesic on a closed non-Euclidean surface of a spherical wedge. We derive the analytic form of the corresponding Poincar\'e map and find…
Billiard models of single particles moving freely in two-dimensional regions enclosed by hard walls, have long provided ideal toy models for the investigation of dynamical systems and chaos. Recently, billiards with (semi-)permeable walls…
A walker is the association of a sub-millimetric bouncing drop moving along with a co-evolving Faraday wave. When confined in a harmonic potential, its stable trajectories are periodic and quantised both in extension and mean angular…
We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of…
We consider classical nonlinear oscillators on hexagonal lattices. When the coupling between the elements is repulsive, we observe coexisting states, each one with its own basin of attraction. These states differ by their degree of…
Wavefunctions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wavefunctions display universal density distributions and density auto-correlations in agreement with…
A R\"ossler model perturbed with a piecewise constant function is investigated. The perturbation function used in the model is constructed by means of the logistic map. In the absence of the perturbation the system is assumed to possess two…
Many classes of active matter develop spatial memory by encoding information in space, leading to complex pattern formation. It has been proposed that spatial memory can lead to more efficient navigation and collective behaviour in…