Perturbations of tempered spectra

ABSTRACT

We show that the tempered spectrum of a sufficiently small perturbation of a sequence of matrices varies little, in the sense that it is contained in a small open neighbourhood of the tempered spectrum of the original sequence. In addition, we show that for perturbations that decay exponentially, all the Lyapunov exponents of the perturbation belong to the tempered spectrum of the original sequence.

KEYWORDS:

• Tempered exponential dichotomy
• tempered spectrum

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 37D99

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by FCT/Portugal through CAMGSD, IST-ID, projects UIDB/04459/2020 and UIDP/04459/2020.