Renormalization, Freezing Phase Transitions and Fibonacci Quasicrystals
Dynamical Systems
2013-10-01 v1
Abstract
We examine the renormalization operator determined by the Fibonacci substitution. We exhibit a fixed point and determine its stable leaf (under iteration of the operator). Then, we study the thermodynamic formalism for po- tentials in this stable leaf, and prove they have a freezing phase transition, with ground state supported on the attracting quasi-crystal associated to the Fibonacci substitution
Keywords
Cite
@article{arxiv.1309.7934,
title = {Renormalization, Freezing Phase Transitions and Fibonacci Quasicrystals},
author = {Henk Bruin and Renaud Leplaideur},
journal= {arXiv preprint arXiv:1309.7934},
year = {2013}
}