Renormalization on One-dimensional Folding Maps
نویسنده
چکیده
Some techniques and results in the renormalization theory of real and complex dynamical systems are summarized. The construction of the induced Markov map of [−1, 1] from a Feigenbaum-like map is presented. We show that this induced Markov map has bounded geometry. We discuss some property of infinitely renormalizable quadratic polynomials and show that the Julia set of an infinitely renormalizable quadratic polynomial satisfying complex a priori bounds is locally connected at its critical point. In addition, if this polynomial is also unbranched, then the Julia set is locally connected. Some result about nonconformal maps and a generalized version of Sullivan’s sector theorem are discussed
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