arXiv:1608.02843 Abstract | arXiv Analytics

arXiv:1608.02843 [math.DS]Abstract References Reviews Resources

What are Lyapunov exponents, and why are they interesting?

Published 2016-08-09Version 1

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, Teichm\"uller theory, and the spectral theory of one-frequency Schr\"odinger 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.

Comments: 27 pages. To appear in the Bulletin of the AMS

Categories: math.DS, math-ph, math.GT, math.MP, math.SP

Subjects: 37C40, 37D25, 37H15, 34D08, 37C60, 47B36, 32G15

Keywords: lyapunov exponents, current events bulletin talk, fields medalist artur avila, smooth ergodic theory, special attention

Related articles: Most relevant | Search more

arXiv:math/0611324 [math.DS] (Published 2006-11-11)

Geometric Expansions, Lyapunov Exponents and Foliations

Radu Saghin, Zhihong Xia

arXiv:1603.06851 [math.DS] (Published 2016-03-22)

Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocycles

Pedro Duarte, Silvius Klein

arXiv:1809.09192 [math.DS] (Published 2018-09-24)