A formula with some applications to the theory of Lyapunov exponents

By Artur Avila, Jairo Bochi. 2001

56 citations recorded by the source corpus.

We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. Indeed, we show that equality holds in Herman’s result. Finally, we give a result about the growth of the spectral radius of products.

Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a1b3818ac0026b65d5dd10b22f70b452f4ae8059

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In Computer Networks and Communications

  1. Artur Avila
  2. J. Yoccoz
  3. Jairo Bochi
  4. Marcelo Viana
  5. Alexander I. Bufetov

In Mathematical Physics

  1. Artur Avila
  2. Marcelo Viana
  3. J. Yoccoz
  4. Jairo Bochi
  5. A. Zorich
  6. David Damanik
  7. G. Forni
  8. Alexander I. Bufetov

In Statistical and Nonlinear Physics

  1. Artur Avila
  2. J. Yoccoz
  3. Marcelo Viana
  4. Jairo Bochi
  5. A. Zorich
  6. David Damanik
  7. Alexander I. Bufetov
  8. G. Forni

Citations in the corpus