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We show that the presence of KAM islands in nonhyperbolic chaotic scattering has deep implications on the unpredictability of open Hamiltonian systems. When the energy of the system increases the particles escape faster. For this reason the…

Chaotic Dynamics · Physics 2019-12-17 Alexandre R. Nieto , Euaggelos E. Zotos , Jesús M. Seoane , Miguel A. F. Sanjuán

We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole…

We study the billiard dynamics in annular tables between two excentric circles. As the center and the radius of the inner circle change, a two parameters map is defined by the first return of trajectories to the obstacle. We obtain an…

Dynamical Systems · Mathematics 2025-07-24 R. B. Batista , M. J. Dias Carneiro , S. Oliffson Kamphorst

Dynamical properties are studied for escaping particles, injected through a hole in an oval billiard. The dynamics is considered for both static and periodically moving boundaries. For the static boundary, two different decays for the…

Chaotic Dynamics · Physics 2015-06-04 Edson D. Leonel , Carl P. Dettmann

We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor…

Chaotic Dynamics · Physics 2013-10-31 J. Solanpaa , J. Nokelainen , P. J. J. Luukko , E. Rasanen

A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to…

Chaotic Dynamics · Physics 2010-08-31 Christian S. Rodrigues , Alessandro P. S. de Moura , Celso Grebogi

We revisit a time-dependent, oval-shaped billiard to investigate a phase transition from bounded to unbounded energy growth. In the static case, the phase space exhibits a mixed structure. The chaotic sea in the static scenario leads to…

Energy spectra of a particle with mass $m$ and charge $e$ in the cubic Aharonov-Bohm billiard containing around $10^4$ consecutive levels starting from the ground state have been analysed. The cubic Aharonov-Bohm billiard is a plane…

chao-dyn · Physics 2009-09-25 Marko Robnik , Jure Dobnikar , Tomaz Prosen

Statistical properties for the recurrence of particles in an oval billiard with a hole in the boundary are discussed. The hole is allowed to move in the boundary under two different types of motion: (i) counterclockwise periodic circulation…

Chaotic Dynamics · Physics 2016-10-12 Matheus Hansen , R. Egydio de Carvalho , Edson D. Leonel

Rounding border effects at the escape point of open integrable billiards are analyzed via the escape times statistics and emission angles. The model is the rectangular billiard and the shape of the escape point is assumed to have a…

Classical Physics · Physics 2015-05-18 MS Custódio , MW Beims

We study the relation between escape rates and pressure in general dynamical systems with holes, where pressure is defined to be the difference between entropy and the sum of positive Lyapunov exponents. Central to the discussion is the…

Dynamical Systems · Mathematics 2011-07-14 Mark Demers , Paul Wright , Lai-Sang Young

We investigate the dependence of the escape rate on the position of a hole placed in uniformly hyperbolic systems admitting a finite Markov partition. We derive an exact periodic orbit formula for finite size Markov holes which differs from…

Chaotic Dynamics · Physics 2013-04-09 Orestis Georgiou , Carl P. Dettmann , Eduardo G. Altmann

A class of non-compact billiards is introduced, namely the infinite step billiards, i.e., systems of a point particle moving freely in the domain $\Omega = \bigcup_{n\in\N} [n,n+1] \times [0,p_n]$, with elastic reflections on the boundary;…

chao-dyn · Physics 2008-02-03 Mirko Degli Esposti , Gianluigi Del Magno , Marco Lenci

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table $\Bi := \bigcup_{n\in\N} [n,n+1] \times…

chao-dyn · Physics 2007-05-23 Mirko Degli-Esposti , Gianluigi Del Magno , Marco Lenci

In open Hamiltonian systems, the escape from a bounded region of phase space according to an exponential decay law is frequently associated with the existence of hyperbolic dynamics in such a region. Furthermore, exponential decay laws…

Chaotic Dynamics · Physics 2021-11-24 Diego S. Fernández , Álvaro G. López , Jesús M. Seoane , Miguel A. F. Sanjuán

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…

Dynamical Systems · Mathematics 2017-04-14 Carl P. Dettmann , Vitaly Fain

Dynamical billiards, or the behavior of a particle traveling in a planar region $D$ undergoing elastic collisions with the boundary, has been extensively studied and is used to model many physical phenomena such as a Boltzmann gas. Of…

Dynamical Systems · Mathematics 2019-10-24 Otto Vaughn Osterman

We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…

Nuclear Theory · Physics 2009-10-31 A. G. Magner , S. N. Fedotkin , K. Arita , T. Misu , K. Matsuyanagi , T. Shachner , M. Brack

The emergence of power laws that govern the large-time dynamics of a one-dimensional billiard of $N$ point particles is analysed. In the initial state, the resting particles are placed in the positive half-line $x\geqslant 0$ at equal…

Statistical Mechanics · Physics 2025-06-26 T. Holovatch , Yu. Kozitsky , K. Pilorz , Yu. Holovatch

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…

Chaotic Dynamics · Physics 2025-05-19 Katherine Holmes , Joseph Hall , Eva-Maria Graefe
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