Diffusion for chaotic sections of 3-periodic surfaces
arxiv.org. math. Cornell University , 2014. No. 1412.7913.
Skripchenko A., Hubert P., Avila A.
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 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 main properties of the Lyapunov spectrum of the corresponding suspension flow.
Research target: Mathematics
Priority areas: mathematics
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