Numerical computation of invariant objects with wavelets [ Back ]

Date:
26.10.15   
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
David Romero
University:
UAB

Abstract:

In certain classes of dynamical systems invariant sets with a strange geometry appear. For example the iteration of two-dimensional quasi-periodically forced skew product, under certain conditions, gives us Strange Non-Chaotic Attractors.

To obtain an analytical approximation of these objects it seems more natural to use wavelets instead of the more usual Fourier approach. The aim of the talk is to describe an algorithm for the semi-analytical computation of the invariant object (numerical computations of the wavelet coefficients) using both Daubechies and Haar wavelets.
The aim for this exercise is to be able to detect, by means of the estimation of the regularity of the object, bifurcations and/or "pinching value" of such object. The study of this regularity (depending on parameters) may give another point of view to the "fractalization routes" described in the literature and that are currently under discussion.

This is a joint work with Lluís Alsedà.