Abstract Chaotic scattering in 2D is well understood employing Smale's horseshoe . For more than 2D we only partially understand such systems . 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.  Jung C et al 2010 New J.Phys. 12 103021.  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.