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**
Chaotic scattering in 2D is well understood employing
Smale's horseshoe [1]. For more than 2D
we only partially understand such systems [2].
We try to salvage some of the knowledge we have for 2D
when increasing the dimensionality. We start
with a problem with some continuous symmetry, say O(2) in a 3D
system and then break this symmetry gradually by an appropriate perturbation,
thus achieving a smooth transition from 2D to 3D.
This works if a) the perturbation conserves the generic generalization
of outer fixed points of a horseshoe to the NHIM (normally hyperbolic
invariant manifold) as defined by Wiggins and b) if at least one degree of
freedom remains closed and corresponds to the symmetry group (e.g. O(2)) of the
unperturbed system. Such a construction is structurally stable and allows to
find the topology of chaotic dynamics, illustrated in a
simple billiard, a battered amphora.
[1] Jung C et al 2010 New J.Phys. 12 103021.
[2] Wiggins S 1994 Normally Hyperbolic Invariant Manifolds in Dynamical
Systems (Springer)

**Seminarsko predavanje bo v petek 23. novembra 2012 ob 15:15 uri
v seminarski sobi CAMTP na Krekovi 2, pritličje desno.
Vljudno vabljeni vsi zainteresirani, tudi študentje.**

Prof.Dr. Marko Robnik

-- Direktor**CAMTP** --

-- Direktor