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What are Lyapunov exponents, and why are they interesting?

This expository paper, based on a Current Events Bulletin talk at the January, 2016 Joint Meetings, introduces the concept of Lyapunov exponents and discusses the role they play in three areas: smooth ergodic theory, Teichmüller theory, and the spectral theory of one-frequency Schrödinger operators. The inspiration for this paper is the work of 2014 Fields Medalist Artur Avila, and his work in these areas is given special attention.

preprint2016arXivOpen access
Amie Wilkinson
math-phmath.DSmath.GTmath.MPmath.SP
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Open access1 author5 topics
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Amie Wilkinson

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