Lyapunov spectrum of square-tiled cyclic covers
By A. Eskin, M. Kontsevich, A. Zorich. 2010
64 citations recorded by the source corpus.
A cyclic cover over the Riemann sphere branched at four points inherits a natural flat structure from the "pillow" flat structure on the basic sphere. We give an explicit formula for all individual Lyapunov exponents of the Hodge bundle over the corresponding arithmetic Teichmuller curve. The key technical element is evaluation of degrees of line subbundles of the Hodge bundle, corresponding to eigenspaces of the induced action of deck transformations.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fab1df7b1fbc6072e733d02a524925b02b6a2da3
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In Geometry and Topology
- Carlos Matheus
- Alexander I. Bufetov
- A. Zorich
- G. Forni
- A. Eskin
- M. Kontsevich
- Martin Moeller
- Marcelo Viana
In Mathematical Physics
- A. Zorich
- Carlos Matheus
- Alexander I. Bufetov
- G. Forni
- A. Eskin
- M. Kontsevich
- Martin Moeller
- Dawei Chen
Citations in the corpus
- Limit theorems for translation flows (2008, methodology): “While, by the Avila-Viana Theorem [4], the Lyapunov spectrum of the Masur-Veech measure is simple, there are also natural examples of invariant measures with nonsimple positive second Lyapunov exponent due to Eskin-Kontsevich-Zorich [17], G.”
- Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow (2011, background): “nvariant suborbifolds of the strata of Abelian differentials in genus two (see [Ba1], [Ba2]) and for certain special Teichmu¨ller curves, the Lyapunov exponents are computed individually, see [BwM¨o], [EKZ], [Fo2], [FMZ1]. 2.2. Sum of Lyapunov exponents. Now we are ready to formulate the principal re”
- Introduction to Teichm\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (2013, background): “t;j) with j2N. However, in some applications41, it is important to determine quantitatively individual exponents of the KZ cocycle. In the case of cyclic covers, A. Eskin, M. Kontsevich and A. Zorich [24] determined the value of (j) for j2P. Roughly speaking, they start the computation (j) = (N j”