# Newhouse phenomena in the Fibonacci trace map

@article{Yessen2015NewhousePI, title={Newhouse phenomena in the Fibonacci trace map}, author={William N. Yessen}, journal={arXiv: Dynamical Systems}, year={2015} }

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…

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