FM 11-13, v.2; arXiv: 1311.5129 v.1

Authors : Giovanni Gallavotti

Title: Random matrices and Lyapunov coefficients regularity

Abstract: Analyticity and other properties of the largest or smallest Lyapunov exponent of a product of real matrices with a ``cone property'' are studied as functions of the matrices entries, as long as they vary without destroying the cone property. The result is applied to stability directions, Lyapunov coefficients and Lyapunov exponents of a class of products of random matrices and of dynamical systems. The method is based on the classical theory of the Mayer series in Statistical Mechanics of rarefied gases.

Keywords: Randm matrices, Statistical Mechanics, Cluster expansion, Lyapunov exponents

Giovanni Gallavotti
INFN Fisica e Accademia dei Lincei
Universita di Roma Sapienza, 00185 Roma, Italy
giovanni.gallavotti@roma1.infn.it, gallavotti@soci-anl.it