Tensor-Based Theory for Quantized Piecewise-Affine Markov Systems: Analysis of Some Map Families

Gianluca SETTI  Riccardo ROVATTI  Gianluca MAZZINI 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E84-A  No.9  pp.2090-2100
Publication Date: 2001/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Chaos & Dynamics
Keyword: 
high-order correlations,  chaotic maps,  tensor algebra,  quantization, 

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Summary: 
In this paper we consider a tensor-based approach to the analytical computation of higher-order expectations of quantized trajectories generated by Piecewise Affine Markov (PWAM) maps. We formally derive closed-form expressions for expectations of trajectories generated by three families of maps, referred to as (n,t)-tailed shifts, (n,t)-broken identities and (n,t,π)-mixing permutations. These families produce expectations with asymptotic exponential decay whose detailed profile is controlled by map design. In the (n,t)-tailed shift case expectations are alternating in sign, in the (n,t)-broken identity case they are constant in sign, and the (n,t,π)-mixing permutation case they follow a dumped periodic trend.