### Citations

88 | Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards. - Sinaı - 1970 |

14 | A new proof of Sinai’s formula for entropy of hyperbolic billiards. Its application to Lorentz gas and stadium, - Chernov - 1991 |

10 |
Numerical experiments on the free motion of a point mass moving in a plane convex region: stochastic transition and entropy
- Benettin, Strelcyn
- 1978
(Show Context)
Citation Context ...al vector ij = (r, sin P). Some numerical results about the KS entropy, the Lyapunov exponents and the mean free time is available in the literature. Let us make a brief report. Benettin and Strelcyn =-=(6)-=- found in 1978 numerical evidence that the KS entropy of a generalized stadium billiard is not a monotone decreasing function of a topological parameter 8 which controls the stadium curvature. In 1984... |

10 |
Numerical study of a ddimensional periodic Lorentz gas with universal properties
- Bouchaud, Doussal
- 1985
(Show Context)
Citation Context ...ior from the infinite horizon one. They claimed, without showing it, that the KS entropy is continuous and they suggested that it is even continuously differentiable.. In 1985 Bouchaud and Le Doussal =-=(8)-=- studied numerically the KS entropy for a two dimensional square lattice billiard. They confirmed the small R behavior found by Friedman et al., (7) in particular they got h = a log P/R with a ^ /? = ... |

9 | Billiards Correlation Functions
- Garrido, Gallavotti
- 1994
(Show Context)
Citation Context ...eraction between mathematical physics and computer experiments has been extremely fruitful in this particular case. In this paper we extend and complete a previous computer experiment about billiards.=-=(1)-=- Our goal is to study the influence of the geometry 1 Institute Carlos I de Fisica Teorica y Computacional, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain. 807 822/88/3-4-18 0022-4... |

8 |
Power-law behavior of Lyapunov exponents in some conservative dynamical systems
- Benettin
- 1984
(Show Context)
Citation Context ...1978 numerical evidence that the KS entropy of a generalized stadium billiard is not a monotone decreasing function of a topological parameter 8 which controls the stadium curvature. In 1984 Benettin =-=(5)-=- studied numerically the Lyapunov exponent for the Diamond billiard as a function of the sides curvature, e. He found that the behavior h^s 1/2 fitted his results very well for all data between 0 <£ <... |

5 |
Soft billiard systems
- Baldwin
- 1988
(Show Context)
Citation Context ...ct, they observe a quasiconstant value of h(S) between R = 0.99 and R = 0.999, before the steep decrease when R is very close to 1. Finally let us mention the works of P. R. Baldwin in 1988 and 1991. =-=(9,10)-=- In the first one he studied numerically an infinite horizon soft billiard system (i.e., the scatterers are regions with a constant potential, U).812 Garrido In particular, he argued that h^In U/R2 w... |

3 | Lectures on the billiards, in "Dynamical systems, theory and applications - Gallavotti - 1975 |

3 |
1991] “The billiard algorithm and KS entropy
- Baldwin
(Show Context)
Citation Context ...ct, they observe a quasiconstant value of h(S) between R = 0.99 and R = 0.999, before the steep decrease when R is very close to 1. Finally let us mention the works of P. R. Baldwin in 1988 and 1991. =-=(9,10)-=- In the first one he studied numerically an infinite horizon soft billiard system (i.e., the scatterers are regions with a constant potential, U).812 Garrido In particular, he argued that h^In U/R2 w... |