Translation surfaces and their orbit closures: an introduction for a broad audience. (English) Zbl 1372.37090
This is an excellent survey and snapshot of the extremely active field of renormalization (i.e., \(\mathrm{GL}(2, \mathbb R)\)) dynamics on the space of translation surfaces. It gives clear motivating examples, elucidates connections to homogenous dynamics, algebraic geometry, and gives a clear introduction to the exciting new developments in the field.
Reviewer: Jayadev Athreya (Seattle)
MSC:
| 37F30 | Quasiconformal methods and Teichmüller theory, etc. (dynamical systems) (MSC2010) |
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
| 30F30 | Differentials on Riemann surfaces |
| 30D05 | Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable |
| 30F60 | Teichmüller theory for Riemann surfaces |
| 14H55 | Riemann surfaces; Weierstrass points; gap sequences |
Keywords:
translation surface; Teichmüller dynamics; abelian differential; Riemann surface; moduli spaceReferences:
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