Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 19, pp. 1-25.

Title: Some applications of Lyapunov regularity
       
Authors: Luis Barreira (Univ. de Lisboa, Lisboa, Portugal)
         Claudia Valls (Univ. de Lisboa, Lisboa, Portugal)

Abstract:
For a non-autonomous dynamics with discrete time defined by a tempered sequence of
upper-triangular matrices, we obtain lower and upper bounds for the Grobman regularity
coefficients.  We also give two applications of these results: we obtain an upper bound
for the Grobman coefficients of the exterior powers of a tempered sequence, and we give
a simple proof of Oseledets' multiplicative ergodic theorem for cocycles over a
measure-preserving transformation without using Kingman's subadditive ergodic theorem. 

Submitted February 11, 2020. Published March 18, 2022.
Math Subject Classifications: 37C75.
Key Words: Lyapunov regularity; exterior powers; cocycles.