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Mathematics > Dynamical Systems

arXiv:1410.2129 (math)
[Submitted on 8 Oct 2014 (v1), last revised 8 May 2015 (this version, v2)]

Title:Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle

Authors:Simion Filip
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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.
Comments: 36 pages
Subjects: Dynamical Systems (math.DS); Geometric Topology (math.GT)
Cite as: arXiv:1410.2129 [math.DS]
  (or arXiv:1410.2129v2 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1410.2129
Journal reference: Duke Math. J. 166, no. 4 (2017), 657-706
Related DOI: https://doi.org/10.1215/00127094-3715806

Submission history

From: Simion Filip [view email]
[v1] Wed, 8 Oct 2014 14:15:05 UTC (31 KB)
[v2] Fri, 8 May 2015 02:33:56 UTC (33 KB)
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