Diffusion rate for windtree models

Teichmüller dynamics mapping class groups and applications
eem2018
Grenoble
[MATH]Mathematics [math]
windtree models
Diffusion rate

Appears in collection : Summer School 2018 - Teichmüller dynamics, mapping class groups and applications.

Recent results on windtree models with polygonal obstacles have linked their diffusion rate with Lyapunov exponents in stata of quadratic differentials. The proves of these theorems follow from the numerous symmetries of the studied examples. In this talk I will present a general method for this purpose in a more general setting using the lattest advances on the structure of the orbit closure of translation surfaces and their Hodge bundle.