Speaker: Itzhak Fouxon
Title: Fractal dimensions of mutlifractals with some applications
Abstract:
We inquire which properties of dissipative systems determine the fractal
dimensions of their strange attractors. It is well known that the system
property that determines the information dimension are the Lyapunov
exponents however there is no similar result for all the dimensions. We
provide a conjecture, similar to the Kaplan-Yorke conjecture, that gives
dimension of an arbitrary order via the statistics of finite time Lyapunov
exponents. We demonstrate that the conjecture agrees with results (some
unknown) in various limits. Some experimental confirmations of the
predictions will be described and question of multifractals formed by rough
flows posed.