Oseledets multiplicative ergodic theorem
Consider a probability measure, and a measure preserving dynamical system. Consider , a measurable transformation, where GL(d,R) is the space of invertible square matrices of size . Consider the multiplicative cocycle defined by the transformation , and assume and are integrable.
such that, for almost everywhere and for all
and and ;
for all ;
Furthermore, the numbers and the subspaces depend measurably on the point .
The numbers are called Lyapunov exponents of relatively to at the point . Each number is called the multiplicity of the Lyapunov exponent . We also have that and , where and are as given by Furstenberg-Kesten theorem.
|Title||Oseledets multiplicative ergodic theorem|
|Date of creation||2014-03-26 14:21:35|
|Last modified on||2014-03-26 14:21:35|
|Last modified by||Filipe (28191)|
|Related topic||Lyapunov exponent|
|Related topic||Furstenberg-Kesten Theorem|