Complex box bounds for real maps
Dynamical Systems
2017-01-06 v3
Abstract
In this paper we prove complex bounds, also referred to as a priori bounds, for real analytic (and even C3) interval maps. This means that we associate to such a map a complex box mapping (which provides a kind of Markov structure), together with universal geometric bounds on the shape of the domains. Such bounds show that the first return maps to these domains are well-controlled, and consequently form one of the corner stones in many recent results on one-dimensional dynamics: renormalisation theory, rigidity results, density of hyperbolicity, local connectivity.
Cite
@article{arxiv.1310.8338,
title = {Complex box bounds for real maps},
author = {Trevor Clark and Sebastian van Strien and Sofia Trejo},
journal= {arXiv preprint arXiv:1310.8338},
year = {2017}
}