Matricial representation of period doubling cascade

Details Matricial representation of period doubling cascade Matricial representation of period doubling cascade

2010-01-18

arxiv.org/abs/1001.3120v1

Nonlinear Sciences

Chaotic Dynamics

20 pages and one figure

Scientific paper

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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