Complex bounds for multimodal maps: bounded combinatorics

Daniel Smania

Keywords: renormalization | multimodal | complex bounds

We prove 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.

Anexos:

• bounds.ps