Naslov
Nonuniform spectrum on the half line and perturbations

Autori
Barreira, Luis ; Dragičević, Davor ; Valls, Claudia

Izvornik
Results in mathematics (1422-6383) 72 (2017), 1/2; 125-143

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

Ključne riječi
Nonuniform hyperbolicity ; spectrum ; perturbations

Sažetak
For a one-sided nonautonomous dynamics defined by a sequence of invertible matrices, we develop a spectral theory (in the sense of Sacker and Sell) for the notion of a nonuniform exponential dichotomy with an arbitrarily small nonuniform part. We emphasize that this notion is ubiquitous in the context of ergodic theory, unlike the notion of a uniform exponential dichotomy. In particular, we show that each Lyapunov exponent belongs to one interval of the spectrum. We also consider a class of sufficiently small nonlinear perturbations of a linear dynamics satisfying a nonuniform bounded growth condition and we show that each solution is either eventually zero or the Lyapunov exponents belong to one interval of the spectrum.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA