Naslov
Chaotic dynamics of two-dimensional billiards with parabolic and elliptical arcs

Autori
Lopac, Vjera

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
AIP Conference Proceedings 795: WOMEN IN PHYSICS: Second IUPAP International Conference on Women in Physics / B. Karplus Hartline, A. Michelman-Ribeiro - : American Institute of Physics (AIP), 2005, 208-208

Skup
WOMEN IN PHYSICS: Second IUPAP International Conference on Women in Physics

Mjesto i datum
Rio de Janeiro, Brazil, 21.05.2005. - 23.05.2005

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
chaotic dynamics; elliptical stadium billiard; parabolic oval billiard; Poincare sections

Sažetak
Dynamical properties of the parabolic oval [1] and elliptical stadium [1-5] billiards are investigated analytically and numerically. These systems exhibit integrable, mixed or fully chaotic behavior, in dependence on the shape parameters. In the elliptical stadium, where our shape parameters are $\delta$ and $\gamma$, calculations confirm the existence of a large fully chaotic region surrounding the straight line $\delta=1-\gamma$ in the parameter space, corresponding to the Bunimovich stadium billiard. The region $\delta<1-\gamma$ with elongated semiellipses has been previously discussed in [4] and [5]. The part of the parameter space for which $\delta>1-\gamma$, comprising the flat semiellipses, has been briefly mentioned in [6]. Here we discuss the results of analysis of diametral orbits of period two, the hour-glass and diamond orbits of period four, and a family of multidiamond orbits of higher periods, as well as the possible predictions for behavior of the leaking billiards of the same type. The quantal statistical properties of the elliptical stadium billiard are also discussed. References: [1] V. Lopac, I. Mrkonji\' c and D. Radi\' c, Phys. Rev. E {;\bf 66};, 035202 (2002) ; [2] V. Lopac, I. Movre, I. Mrkonji\' c and D. Radi\'c, Prog. Theor. Phys. Suppl. {;\bf 150};, 371 (2003) ; [3] V. Lopac, I. Mrkonji\' c, N. Pavin and D. Radi\'c, to be published ; [4] E. Canale, R. Markarian, S. Oliffson Kamphorst and S. Pinto del Carvalho, Physics D {;\bf 115};, 189 (1998) ; [5] S. Oliffson Kamphorst and S. Pinto del Carvalho, Discr. and Cont. Dynam. Syst. {;\bf 7};, 663 (2001) ; [6] M. Wojtkowski, Commun. Math. Phys. {;\bf 105};, 391 (1986).

Izvorni jezik
Engleski

Znanstvena područja
Fizika

POVEZANOST RADA