Construction of a Piecewise Linear One-Dimensional Map Generating an Arbitrary Prescribed Tree Source

Yasutada OOHAMA  Mariko SUEMITSU  Tohru KOHDA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A    No.9    pp.2251-2255
Publication Date: 2003/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Nonlinear Theory and its Applications)
dynamical systems,  tree sources,  Markov sources,  piecewise-linear maps,  

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We consider the problem of constructing nonlinear dynamical systems that realize an arbitrary prescribed tree sources. We give a construction of dynamical systems by using piecewise-linear maps. Furthermore, we examine the obtained dynamical system to show that the structure of the memory of tree sources is characterized with some geometrical property of the constructed dynamical systems. Using a similar method, we also construct a dynamical system generating an arbitrary prescribed reverse tree source and show that the obtained dynamical system has some interesting geometrical property explicitly reflecting the tree structure of the memory of the reverse tree source.