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LIMIT THEOREMS FOR DISPERSING BILLIARDS WITH CUSPS
Dispersing billiards Sinai billiards cusps
2015/9/29
Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic patterns. Their statisti...
CONVERGENCE OF MOMENTS FOR DISPERSING BILLIARDS WITH CUSPS
Chaos decay of correlations Central Limit Theorem
2015/9/29
Dispersing billiards with cusps are deterministic dnamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic paterns.
Mathematical theory of billiards is a fascinating subject providing a fertile source of new problems as well as conjecture
testing in dynamics, geometry, mathematical physics and spectral
theory. Th...
Classical dynamics and particle transport in kicked billiards
Classical dynamics particle transport kick source momentum
2011/7/6
We study nonlinear dynamics of the kicked particle whose motion is confined by square billiard. The kick source is considered as localized at the center of square with central symmetric spatial distri...
Spectral Statistics of "Cellular" Billiards
Chaotic Dynamics(nlin.CD) Mathematical Physics(math-ph) Spectral Theory(math.SP)
2010/11/10
For a bounded planar domain $\Omega^0$ whose boundary contains a number of flat pieces $\Gamma_i$ we consider a family of non-symmetric billiards $\Omega$ constructed by patching several copies of $\O...
Doorway States and Billiards
States Billiards
2010/11/10
Whenever a distinct state is immersed in a sea of complicated and dense states, the strength of the distinct state, which we refer to as a doorway, is distributed in their neighboring states. We analy...
Two-valued groups, Kummer varieties and integrable billiards
Two-valued groups Kummer varieties integrable billiards
2010/11/18
A natural and important question of study two-valued groups associated with hyperelliptic Jacobians and their relationship with integrable systems is motivated by seminal examples of relationship bet...
Inspired by the work of Pujals and Sambarino on dominated splitting, we present billiards with a modi ed re ection law which constitute simple examples of dynamical systems with limit sets with domina...
Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards
cosine law stochastic billiard Knudsen random wal random medium random walk in random environment unbounded
2010/11/26
We consider a random walk in a stationary ergodic environment
in Z, with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of s...
Invisibility in billiards
Billiards shape optimization problems of minimal resistance classical scattering Newtonian aerodynamics invisible bodies
2010/11/30
The question of invisibility for bodies with mirror surface is studied in the frame-work of geometrical optics. We construct bodies that are invisible/have zero resis-tance in two mutually orthogonal ...
Stable and unstable regimes in higher-dimensional convex billiards with cylindrical shape
Stable unstable regimes higher-dimensional cylindrical shape
2010/12/15
We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders c...