Diffusion for chaotic plane sections of 3-periodic surfaces

Artur Avila, Pascal Hubert, Alexandra Skripchenko

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)109-146
Number of pages38
JournalInventiones Mathematicae
Issue number1
Publication statusPublished - 1 Oct 2016
Externally publishedYes


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