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On the Lyapunov exponents of the Kontsevich-Zorich cocycle. (English) Zbl 1130.37302

Hasselblatt, B.(ed.) et al., Handbook of dynamical systems. Volume 1B. Amsterdam: Elsevier (ISBN 0-444-52055-4/hbk). 549-580 (2006).
From the introduction: The Kontsevich-Zorich cocycle is a cocycel over the Teichmüller flow on the moduli space of holomorphic (quadratic) differentials. The study of the dynamics of this cocycle, in particular of its Lyapunov structure, has important applications to the ergodic theory of interval exchange transformations (i.e.t.’s) and related systems such as measured foliations, flows on translation surfaces and rational polygonal billiards. The Kontsevich-Zorich cocycle is a continuous- time version of a cocycle introduced by G. Rauzy [Acta Arith. 34, 315–328 (1979; Zbl 0414.28018)] as a “continued fraction algorithm” and later studied by W. A. Veech in his work on the unique ergodicity of the generic i.e.t. [Ann. Math. (2) 115, 201–242 (1982; Zbl 0486.28014)] and A. Zorich, Ann. Inst. Fourier 46, 325–370 (1996; Zbl 0853.28007)], among others.
For the entire collection see [Zbl 1081.00006].

MSC:

37Axx Ergodic theory
37Cxx Smooth dynamical systems: general theory
37Fxx Dynamical systems over complex numbers
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