Related papers: Numerical study of a three-dimensional generalized…
The multidimensional cosmological model describing the evolution of $n$ Einstein spaces in the presence of multicomponent perfect fluid is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the…
Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically off a boundary curve. The state of the system is given by two numbers: one describing the location along the curve where the bounce occurs, and…
We call a system bouncing ball billiard if it consists of a particle that is subjected to a constant vertical force and bounces inelastically on a one-dimendional vibrating periodically corrugated floor. Here we choose circular scatterers…
The effect of boundary deformation on the non-separable entanglement which appears in the classical elec- tromagnetic field is considered. A quantum chaotic billiard geometry is used to explore the influence of a mechanical modification of…
In this paper we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a 2-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism,…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…
A system of two masses connected with a weightless rod (called dumbbell in this paper) interacting with a flat boundary is considered. The sharp bound on the number of collisions with the boundary is found using billiard techniques. In…
We study the dielectric annular billiard as a quantum chaotic model of a micro-optical resonator. It differs from conventional billiards with hard-wall boundary conditions in that it is partially open and composed of two dielectric media…
We extended a previous qualitative study of the intermittent behaviour of a chaotical nucleonic system, by adding a few quantitative analyses: of the configuration and kinetic energy spaces, power spectra, Shannon entropies, and Lyapunov…
We perform a detailed numerical study of diffusion in the $\varepsilon$ stadium of Bunimovich, and propose an empirical model of the local and global diffusion for various values of $\varepsilon$ with the following conclusions: (i) the…
An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is found that the set of 3-period orbits in billiards on…
Lensed billiards are an extension of the notion of billiard dynamical systems obtained by adding a potential function of the form $C1_{\mathcal{A}}$, where $C$ is a real valued constant and $1_{\mathcal{A}}$ is the indicator function of an…
We show that a generic analytic strongly convex billiard is "maximally chaotic" in the sense that, for every rational number $\frac{p}{q} \in \mathbb{Q} \cap (0,1)$, all intersections between the stable and unstable manifolds of maximizing…
We study a class of dynamical systems which generalizes and unifies some models arising in the analysis of switched flow systems in manufacturing. General properties of these dynamical systems, called pseudo billiards, as well as some their…
We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…
The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the…
The dynamics in three-dimensional billiards leads, using a Poincar\'e section, to a four-dimensional map which is challenging to visualize. By means of the recently introduced 3D phase-space slices an intuitive representation of the…
We analyze the dynamics of the Mixmaster Universe on the base of a standard Arnowitt-Deser-Misner Hamiltonian approach showing how its asymptotic evolution to the cosmological singularity is isomorphic to a billiard on the Lobachevsky…
We construct an autonomous chaotic Hamiltonian ratchet as a channel billiard subdivided by equidistant walls attached perpendicularly to one side of the channel, leaving an opening on the opposite side. A static homogeneous magnetic field…
The escape of an ensemble of particles from the Bunimovich stadium via a small hole has been studied numerically. The decay probability starts out exponentially but has an algebraic tail. The weight of the algebraic decay tends to zero for…