Complex bounds for multimodal maps: bounded combinatorics

Abstract

We proved the so called complex bounds for multimodal, infinitely renormalizable analytic maps with bounded combinatorics: deep renormalizations have polynomial-like extensions with definite modulus. The complex bounds is the first step to extend the renormalization theory of unimodal maps to multimodal maps.

20 pages, 3 figures

Cited by in corpus (4)

• Complex a priori bounds for multicritical circle maps with bounded type rotation number
• Topological obstructions to smoothness for infinitely renormalizable maps of the disk
• The boundary of chaos for interval mappings
• Renormalization of symmetric bimodal maps with low smoothness