No hyperbolic sets in J_\infty for infinitely renormalizable quadratic polynomials
Dynamical Systems
2022-06-22 v2
Abstract
Let f be an infinitely-renormalizable quadratic polynomial and J_\infty be the intersection of forward orbits of "small" Julia sets of simple renormalizations of f. We prove that J_\infty contains no hyperbolic sets.
Cite
@article{arxiv.2107.11962,
title = {No hyperbolic sets in J_\infty for infinitely renormalizable quadratic polynomials},
author = {Genadi Levin and Feliks Przytycki},
journal= {arXiv preprint arXiv:2107.11962},
year = {2022}
}
Comments
Final version: extended, a corollary added, and the title changed. To appear