English

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

R2 v1 2026-06-24T04:30:47.892Z