Conjugation of cascades

Jesus San Martin; Daniel Rodriguez-Perez

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arXiv · nlin/0612007

Conjugation of cascades

Jesus San Martin·Daniel Rodriguez-Perez

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Abstract

Presented in this work are some results relative to sequences found in the logistic equation bifurcation diagram, which is the unimodal quadratic map prototype. All of the different saddle-node bifurcation cascades, associated to every last appearance p-periodic orbit (p=3,4,5,...), can also be generated from the very Feigenbaum cascade. In this way it is evidenced the relationship between both cascades. The orbits of every saddle-node bifurcation cascade, mentioned above, are located in different chaotic bands, and this determines a sequence of orbits converging to every band-merging Misiurewicz point. In turn, these accumulation points form a sequence whose accumulation point is the Myrberg-Feigenbaum point. It is also proven that the first appearance orbits in the n-chaotic band converge to the same point as the last appearance orbits of the (n+1)-chaotic band. The symbolic sequences of band-merging Misiurewicz points are computed for any window.

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BibTeX RIS

Jesus San Martin, Daniel Rodriguez-Perez. 2006-12-04. Conjugation of cascades. https://arxiv.org/abs/nlin/0612007

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