CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS
UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR
KREKOVA 2 SI-2000 MARIBOR SLOVENIA
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Robnik@uni-mb.si $\bullet$ www.camtp.uni-mb.si
PROF.DR. MARKO ROBNIK, DIRECTOR

Seminarsko predavanje
Centra za uporabno matematiko in teoreticno fiziko

Analysis of the orbit stability in some classes of billiards with the hyperbolic, elliptical and parabolic boundary arcs

Profesor Dr. Vjera Lopac
Division of Physics, Faculty of Chemical Engineering and Technology
University of Zagreb, Croatia

Abstract: By calculating the Poincaré sections and the traces of the deviation matrix, we investigate the chaotic behavior of several classes of lemon shaped planar billiards $[1-3]$ in dependence on the shape parameter. Similar methods are also applied to a large class of billiards with discontinuities in the curvature of the boundary, including the elliptical stadium $[4,5]$ and a new family of parabolic oval billiards. The stability of some important periodic orbits determining the phase space structure is calculated, and their effect on the separation of the chaotic region into several chaotic components is discussed. Some results concerning the comparison of classical and quantum results are presented.
References: $[1]$ V. Lopac et al Phys. Rev. E59, 303 (1999);$[2]$I. Mrkonjic et al Prog. Theor. Phys. Suppl. 139, 382 (2000); $[3]$ V. Lopac et al Phys. Rev. E64, 016214 (2001); $[4]$ V. Donnay, Comm. Math. Phys. 141, 225 (1991); $[5]$ S.O. Kamphorst et al, Discrete & Continuous Dynamical Systems 7, 663 (2001)

Seminarsko predavanje bo v cetrtek 13. decembra ob 17:15 uri v seminarski sobi CAMTP, Krekova 2, priticje desno. Vljudno vabljeni vsi zainteresirani, tudi študentje.

Prof.Dr. Marko Robnik
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