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 teoretično fiziko

Chaotic scattering beyond two dimension

Professor Dr. Thomas Seligman

Physics Department, University of Ljubjana, Permanent address: Instituto de Ciencias Fisicas, University of Mexico, Cuernavaca, Mexico

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
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