Related papers: A classification of classical billiard trajectorie…
We consider three-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We…
The study of polygonal billiards, particularly those in the regular pentagon, has been the subject of two recent papers. One of these papers approaches the problem of discovering the periodic trajectories on the pentagon by identifying…
We present polynomial Poisson algebras for the 8 classical potentials in two-dimensional Euclidian space that separate in cartesian coordinates and allow a third order integral of motion. Some of the classical superintegrale potentials do…
We derive necessary and sufficient conditions for periodic and for elliptic periodic trajectories of billiards within an ellipse in the Minkowski plane in terms of an underlining elliptic curve. We provide several examples of periodic and…
We consider the free motion of a point particle inside a circular billiard with periodically moving boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the energy of the particle is not…
Exact results for three trajectories of small numbers of particles interacting hydrodynamically through Stokeslets are presented. First, the middle particle in a vertical trio of particles sediments at a constant velocity for all time.…
In this paper we proved that under the Lazutkin's coordinate, the billiard map can be interpolated by a time-1 flow of a Hamiltonian $H(x,p,t)$ which can be formally expressed by \[…
Past studies of the billiard-ball paradox, a problem involving an object that travels back in time along a closed timelike curve (CTC), typically concern themselves with entirely classical histories, whereby any trajectorial effects…
I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and…
In this paper, we introduced the 3D-Quantum Stationary Hamilton Jacobi Equation for a central potential, and established the 3D quantum law of motion of an electron in the presence of such a potential. We established a system of three…
We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
We introduce and prove numerous new results about the orbits of the $T$-fractal billiard. Specifically, in Section 3, we give a variety of sufficient conditions for the existence of a sequence of compatible periodic orbits. In Section 4, we…
Classical-quantum correspondence for conservative chaotic Hamiltonians is investigated in terms of the structure of the eigenfunctions and the local density of states, using as a model a 2D rippled billiard in the regime of global chaos.…
We introduce a class of billiards with chaotic unidirectional flows (or non-chaotic unidirectional flows with "vortices") which go around a chaotic or non-chaotic "core", where orbits can change their orientation. Moreover, the…
A lower bound for the number of 3-periodical billiard trajectories in a manifold embedded in Euclidean space is obtained.
We present a remarkable discretization of the classical Kepler problem which preserves its trajectories and all integrals of motion. The points of any discrete orbit belong to an appropriate continuous trajectory.
We study the stability of periodic trajectories of planar inverse magnetic billiards, a dynamical system whose trajectories are straight lines inside a connected planar domain $\Omega$ and circular arcs outside $\Omega$. Explicit examples…
We rigorously investigate closed Minkowski/Finsler billiard trajectories on $n$-dimensional convex bodies. We outline the central properties in comparison and differentiation from the Euclidean special case and establish two main results…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…