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We describe all the situations in which the Kontsevich-Zorich cocycle has zero Lyapunov exponents. Confirming a conjecture of Forni, Matheus, and Zorich, this only occurs when the cocycle satisfies additional… Click to show full abstract
We describe all the situations in which the Kontsevich-Zorich cocycle has zero Lyapunov exponents. Confirming a conjecture of Forni, Matheus, and Zorich, this only occurs when the cocycle satisfies additional geometric constraints. We also describe the real Lie groups which can appear in the monodromy of the Kontsevich-Zorich cocycle. The number of zero exponents is then as small as possible, given its monodromy.
Keywords:
monodromy kontsevich;
zorich cocycle;
cocycle;
kontsevich zorich;
lyapunov exponents;
zero lyapunov
Journal Title: Duke Mathematical Journal
Year Published: 2017
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Journal Title: Duke Mathematical Journal
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!