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arXiv · 1507.07912

Newhouse phenomena in the Fibonacci trace map

William Yessen
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Abstract

We study dynamical properties of the Fibonacci trace map - a polynomial map that is related to numerous problems in geometry, algebra, analysis, mathematical physics, and number theory. Persistent homoclinic tangencies, stochastic sea of full Hausdorff dimension, infinitely many elliptic islands - all the conservative Newhouse phenomena are obtained for many values of the Fricke-Vogt invariant. The map has all the essential properties that were obtained previously for the Taylor-Chirikov standard map, and can be suggested as another candidate for the simplest conservative system with highly non-trivial dynamics.

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William Yessen. 2015-07-28. Newhouse phenomena in the Fibonacci trace map. https://arxiv.org/abs/1507.07912

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