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 investigate the formation and destruction of resonance islands in (generalized) mushroom billiards, which are a recently discovered class of Hamiltonian systems with mixed regular-chaotic dynamics. In the few-particle case, we compare the dynamics in container geometries whose counterpart one-particle billiards are integrable, chaotic, and mixed. One of our findings is that two-, three-, and four-particle billiards confined to containers with integrable one-particle counterparts inherit some integrals of motion and exhibit a regular partition of phase space into ergodic components of positive measure. Therefore, the shape of a container matters not only for noninteracting particles but also for interacting particles.
Skip Nav Destination
Article navigation
March 2006
Research Article|
March 30 2006
One-particle and few-particle billiards
Steven Lansel;
Steven Lansel
School of Electrical and Computer Engineering and School of Mathematics,
Georgia Institute of Technology
, Atlanta, Georgia 30332-0160
Search for other works by this author on:
Mason A. Porter;
Mason A. Porter
Department of Physics and Center for the Physics of Information,
California Institute of Technology
, Pasadena, California 91125-3600
Search for other works by this author on:
Leonid A. Bunimovich
Leonid A. Bunimovich
School of Mathematics and Center for Nonlinear Science,
Georgia Institute of Technology
, Atlanta, Georgia 30332-0160
Search for other works by this author on:
Chaos 16, 013129 (2006)
Article history
Received:
August 29 2005
Accepted:
November 03 2005
Citation
Steven Lansel, Mason A. Porter, Leonid A. Bunimovich; One-particle and few-particle billiards. Chaos 1 March 2006; 16 (1): 013129. https://doi.org/10.1063/1.2147740
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Pay-Per-View Access
$40.00
Citing articles via
Recent achievements in nonlinear dynamics, synchronization, and networks
Dibakar Ghosh, Norbert Marwan, et al.
Sex, ducks, and rock “n” roll: Mathematical model of sexual response
K. B. Blyuss, Y. N. Kyrychko
Nonlinear model reduction from equations and data
Cecilia Pagliantini, Shobhit Jain
Related Content
Two-particle circular billiards versus randomly perturbed one-particle circular billiards
Chaos (February 2013)
Ergodicity of the generalized lemon billiards
Chaos (December 2013)
Stability and ergodicity of moon billiards
Chaos (August 2015)
No-slip billiards with particles of variable mass distribution
Chaos (February 2022)
Survival probability for open spherical billiards
Chaos (November 2014)