Nonuniform Spectrum on the Half Line and Perturbations

作者：Barreira Luis^*; Dragicevic Davor; Valls Claudia

来源：Results in Mathematics, 2017, 72(1-2): 125-143.

DOI：10.1007/s00025-016-0626-8

• Nonuniform hyperbolicity
• spectrum
• perturbations

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.

• 出版日期2017-9