Related papers: Billiard in the space with a time machine

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary, and also a circular scatterer in the interior of the disk. We investigate stability properties of some…

Can elliptic islands contribute to sustained energy growth as parameters of a Hamiltonian system slowly vary with time? In this paper we show that a mushroom billiard with a periodically oscillating boundary accelerates the particle inside…

We study linear nonautonomous parabolic systems with dynamic boundary conditions. Next, we apply these results to show a theorem of local existence and uniqueness of a classical solution to a second order quasilinear system with nonlinear…

The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…

Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…

We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…

We investigate symmetry breaking in a time-dependent billiard that undergoes a continuous phase transition when dissipation is introduced. The system presents unlimited velocity, and thus energy growth for the conservative dynamics. When…

We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…

In a realistic scenario, the evolution of the rotational dynamics of a celestial or artificial body is subject to dissipative effects. Time-varying non-conservative forces can be due to, for example, a variation of the moments of inertia or…

Light propagation on a two-dimensional curved surface embedded in a three-dimensional space has attracted increasing attention as an analog model of four-dimensional curved spacetime in laboratory. Despite recent developments in modern…

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Several simple models of table motion are studied and compared. Dependence of displacement of the table on time,…

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,…

In this paper we are interested in the motion of a ball inside a billiard table bounded by a particular smooth curve. This table belongs to a family of billiards which can all be drawn by a common process: the so-called gardener's string…

Systems of pinned billiard balls serve as simplified models of collisions, where all particles remain fixed in their positions while their (pseudo-)velocities evolve in accordance with the laws of conservation of energy and momentum. For…

Active systems are comprised of constituents with interactions that are generically non-reciprocal in nature. Such non-reciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing…

In two recent articles a detailed study has been presented of the out of equilibrium dynamics of an infinite system of self-gravitating points initially located on a randomly perturbed lattice. In this article we extend the treatment of the…

The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…

A periodic trajectory on a polygonal billiard table is stable if it persists under any sufficiently small perturbation of the table. It is a standard result that a periodic trajectory on an $n$-gon gives rise in a natural way to a closed…

We study the dynamics of a bouncing coin whose motion is restricted to the two-dimensional plane. Such coin model is equivalent to the system of two equal masses connected by a rigid rod, making elastic collisions with a flat boundary. We…