Matricial representation of period doubling cascade

2010/01/18 by Lucia Cerrada, Cerrada, Lucia, Jesus San Martin +1
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #nlin.CD

paper · pdf · doi:10.48550/arxiv.1001.3120

20 pages and one figure

arxiv created 2010/01/18 · arxiv updated 2010/02/26

Abstract

Starting from the cycle permutation sigma_(2^k) associated with the (2^k)-periodic orbit of the period doubling cascade we obtain the inverse permutation (sigma_(2^k))^-1. Then we build a matrix permutation related to (sigma_(2^k))^-1, which includes the visiting order of the (2^k)-periodic orbit points. After some manipulations a recurrence relation of matricial representation of period doubling cascade is obtained. Finally the explicit matricial representation is reached.

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