engleski

A note on the theorem of Johnson, Palmer and Sell

The well-known theorem of Johnson, Palmer and Sell as- serts that the endpoints of the Sacker-Sell spectrum of a given cocycle A over a topological dynamical system (M, f ) are realized as Lyapunov exponents with respect to some ergodic invariant probability measure for f . The main purpose of this note is to give an alternative proof of this theorem which uses a more recent and independent result of Cao which formulates sufficient conditions for the uniform hyperbolicity of a given cocyle A in terms of the nonvanishing of Lyapunov exponents for A. We also discuss the possibility of obtaining positive results related to the stability of the Sacker-Sell spectra under the perturbations of the cocycle A.

Sacker-Sell spectrum ; Lyapunov exponents ; Invariant measures ; stability

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