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Adjacency and Parity Relations of Words in Discrete Dynamical Systems

✍ Scribed by William Y.C. Chen; James D. Louck; Jun Wang

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 222 KB
Volume: 91
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3112

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✦ Synopsis

Words on two letters, or their equivalent representation by : sequences, label the branches of the inverse graph of the n th iterate of the parabolic map p (x) = x(2&x) of the real line. The abstract properties of words control the evolution of this graph in the content parameter . In particular, properties of words (: sequences) control the process of creation and bifurcation of fixed points. The subset of lexical words of length n&1 or the corresponding set of lexical : sequences of degree D=n&1 are key entities in this description, as are the divisor set of lexical words of degree D such that 1+D divides n. The parity, even or odd, of the length of the lexical sequences in the divisor set controls the motion, from left to right or right to left, of the central point (1, x()) of the inverse graph through the midpoint (1, 1), as the content parameter `increase.

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