Renormalization of almost commuting pairs
Dynamical Systems
2019-11-13 v5
Abstract
In this paper we give a new prove of hyperbolicity of renormalization of critical circle maps using the formalism of almost-commuting pairs. We extend renormalization to two-dimensional dissipative maps of the annulus which are small perturbations of one-dimensional critical circle maps. Finally, we demontsrate that a two-dimensional map which lies in the stable set of the renormalization operator possesses an attractor which is topologically a circle. Such a circle is critical: the dynamics on it is topologically, but not smoothly, conjugate to a rigid rotation.
Keywords
Cite
@article{arxiv.1604.00719,
title = {Renormalization of almost commuting pairs},
author = {Denis Gaidashev and Michael Yampolsky},
journal= {arXiv preprint arXiv:1604.00719},
year = {2019}
}