No hyperbolic sets in J_\infty for infinitely renormalizable quadratic polynomials

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.

Final version: extended, a corollary added, and the title changed. To appear