Kuo-Chiang Tan
Published 2012-07-15Version 1
In this paper, we use permutation elements to record cylinder decompositions of a square-tiled surface $X$. Collecting all such possible permutation elements that record cylinder decompositions, we can enumerate the $SL_2(\mathbb{Z})$ orbit of a given surface $X$ and give a method to determine whether or not a matrix $A\in SL_2(\mathbb{Z})$ is the differential of an affine diffeomorphism of $X$.
A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces
Cutting sequences on square-tiled surfaces
Reducibility of quantum harmonic oscillator on $ R^d$ with differential and quasi-periodic in time potential
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