Newhouse phenomena in the Fibonacci trace map
Dynamical Systems
2015-07-29 v1
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.
Cite
@article{arxiv.1507.07912,
title = {Newhouse phenomena in the Fibonacci trace map},
author = {William Yessen},
journal= {arXiv preprint arXiv:1507.07912},
year = {2015}
}
Comments
45 pages, 8 figures, 81 references