martedi' 22-11-2005 (14:00) - sala conferenze del Centro di Ricerca Matematica Ennio de Giorgi Yutaka ISHII ((Kyushu University)) : Hyperbolic polynomial diffeomorphisms of C^2

Abstract.1 (ISHII): In this talk I will explain a general framework for verifying hyperbolicity of holomorphic dynamical systems in C^2. This framework in particular enables us to construct the first example of a hyperbolic complex H'enon map which cannot be topologically conjugate on its Julia set to a small perturbation of any expanding polynomial in one complex variable. Some applications to the analysis of (the maximal entropy and horseshoe) parameter loci for the H'enon family in R^2 will be also given.

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mercoledi' 23-11-2005 (14:00) - sala conferenze del Centro di Ricerca Matematica Ennio de Giorgi A. Shudo (Tokyo Metropolitan University) : Complex classical dynamics and quantum tunneling in the presence of chaos

Abstract. Phase space of multi-dimensional Hamiltonian systems is generally composed of infinitely many invariant components. The orbits in classical mechanics are always confined on the corresponding invariant set by definition, in particular, except in case of ideal chaotic systems, there are orbits with positive measure that move only on the limited subspace whose dimension is less than that of the full phase space.

On the other hand, the wavepacket of quantum mechanics is not forced to stay on a certain limited classical manifold, but spreads over or share different invariant subsets simultaneously. The spreading is a consequence of the wave effect which make a sharp contrast to classical dynamics. There is not any obstacle in principle preventing the transition between arbitrary two points in the phase space and the quantum wavepacket can penetrate into any kinds of barriers. Such a classically forbidden process does not have no classical counterparts and called "dynamical tunneling" in the literature.

Here we shall present how complex classical trajectories describing dynamical tunneling are tightly related to several key objects in the theory of complex dynamical systems.

Giulia Curciarello Segreteria Didattica tel: 050-2213219 e-mail curciare@dm.unipi.it

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