Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2010-01-18
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.
Cerrada Lucia
Martin Jesus San
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