CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS
UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR
KREKOVA 2 SI-2000 MARIBOR SLOVENIA
Phone +(386) (2) 2355 350 and 2355 351 $\bullet$ Fax +(386) (2) 2355 360
Robnik@uni-mb.si $\bullet$ www.camtp.uni-mb.si
PROF.DR. MARKO ROBNIK, DIRECTOR

Seminarsko predavanje
Centra za uporabno matematiko in teoreticno fiziko

Elliptic islands in a family of billiard systems

Dr. Arnd Bäcker

Abteilung für Theoretische Physik
Universität Ulm
Albert Einstein-Allee 11, D-89069 Ulm, Germany

Abstract By continuation from the hyperbolic limit of the cardioid billiard we show that there is an abundance of bifurcations in the family of limacon billiards. The statistics of these bifurcations show that the sizes of the stable intervals decrease with approximately the same rate as their number increases with the period. In particular, we give numerical evidence that arbitrarily close to the cardioid there are elliptic islands due to orbits created in saddle node bifurcations. This shows explicitly that if in this one parameter family of maps ergodicity occurs for more than one parameter the set of these parameter values has a complicated structure.
Reference:H. R. Dullin and A. Bäcker: About ergodicity in the family of limacon billiards, Nonlinearity 11 (2001) 79-87
http://www.physik.uni-ulm.de/theo/qc/baec/

Seminarsko predavanje bo v cetrtek, 13. decembra 2001 ob 15:15 uri v seminarski sobi CAMTP, Krekova 2, pritlicje. Vljudno vabljeni vsi zainteresirani, tudi študentje.

Prof.Dr. Marko Robnik
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