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The Center for Control, Dynamical Systems, and Computation University of California at Santa Barbara
 

Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Fall 2006 Seminars
Presents
Information Technology Applications of
Statistical Nonlinear Dynamics
by Prof. Gianluca Setti
University of Ferrara, Italy
Friday, November 3rd, 2006 3:00 - 4:00 PM Frank Hall 4164
Abstract:
Recent developments have highlighted that a statistical approach may greatly benefit the study of discrete-time chaotic
system (maps). In this case, in fact, critical dependence on initial condition, probably the widest known feature of chaotic
behavior, prevents the study of single trajectories from giving information which are globally valid. On the contrary, a highly
regular behaviour exists for the distribution of the points describing the evolution of a set of trajectories at each iteration
step. We will formalize this approach by introducing a theoretical framework that is based on the classical Perron-Frobe-
nius Operator (PFO), which accounts for the evolution of the probability densities describing the distribution of the system
state variable at each iteration step. We then focus on Piecewise Affine Markov (PWAM) maps, and by specializing the
set of theoretical tools that we have introduced, we will show how such maps can be considered as stochastic processes
generators with tunable statistical features. Such a well-developed theoretical framework can be applied to several topics
related to IT, such as

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics