Representation of period doubling by digraphs and characteristic polynomials

Yoshifumi Takenouchi; Richell Celeste

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arXiv · 0909.0335

Representation of period doubling by digraphs and characteristic polynomials

Yoshifumi Takenouchi·Richell Celeste

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Abstract

A general procedure which defines a partial ordering of cyclic permutations induced by continuous maps is known for constructing immediate successors to a cycle. We expound on this procedure in terms of labelled digraphs and characteristic polynomials then apply this study to period doubling, the most common route to chaos for a nonlinear dynamical system.

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Yoshifumi Takenouchi, Richell Celeste. 2009-09-02. Representation of period doubling by digraphs and characteristic polynomials. https://arxiv.org/abs/0909.0335

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