Diffusion for chaotic plane sections of 3-periodic surfaces
Dynamical Systems
2016-03-25 v3
Abstract
We study chaotic plane sections of some particular family of triply periodic surfaces. The question about possible behavior of such sections was posed by S. P. Novikov. We prove some estimations on the diffusion rate of these sections using the connection between Novikov's problem and systems of isometries - some natural generalization of interval exchange transformations. Using thermodynamical formalism, we construct an invariant measure for systems of isometries of a special class called the Rauzy gasket, and investigate the main properties of the Lyapunov spectrum of the corresponding suspension flow.
Cite
@article{arxiv.1412.7913,
title = {Diffusion for chaotic plane sections of 3-periodic surfaces},
author = {Artur Avila and Pascal Hubert and Alexandra Skripchenko},
journal= {arXiv preprint arXiv:1412.7913},
year = {2016}
}
Comments
31 pages, 11 figures. arXiv admin note: text overlap with arXiv:1311.5361. in Inventiones mathematicae, 2016