Naslov
A note on the theorem of Johnson, Palmer and Sell

Autori
Dragičević, Davor

Izvornik
Periodica mathematica Hungarica (0031-5303) 75 (2017), 2; 167-171

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA