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 Fax +(386) (2) 2355 360

Robnik@uni-mb.si www.camtp.uni-mb.si

PROF.DR. MARKO ROBNIK, DIRECTOR

**Abstract**:
The interest in understanding the dynamics of billiard problems goes back
to the work of Birkhoff in 1927. Inside the billiard, a point particle is
freely moving along a straight line until it hits the boundary.
Upon the
collision, it is assumed that the particle is specularly reflected. In our
work, we revisit the problem of a billiard particle bouncing inside a
periodically time varying oval billiard and study the aspects of
Fermi acceleration. The problem is described using a
four dimensional mapping.
Our main goal
is to understand and describe the behaviour of the particle's average
velocity (and hence its energy - Fermi acceleration) as a function of the number of collisions
and to study the effects of dissipation.
We observed that depending on what
kind of dissipation we introduce one can observe different asymptotic
behaviours including transients, attracting fixed points and locking, chaotic
attractors and even crisis events as the damping coefficients are varied.
**References:** E. D. Leonel, D. F. M. Oliveira, A. Loskutov, *Chaos*.
**19**, (2009) 033142(1-11);
D. F. M. Oliveira, E. D. Leonel, *Physica A.* accepted for
publication, 2009.

**Seminarsko predavanje (v angleškem jeziku)
bo v četrtek 18. februarja 2010 15:15 uri
v seminarski sobi CAMTP na Krekovi 2, pritličje desno.
Vljudno vabljeni vsi zainteresirani, tudi študentje.**

Prof.Dr. Marko Robnik

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