A Rolewicz-type characterization of nonuniform behaviour

ABSTRACT

We present necessary and sufficient conditions in the spirit of Rolewicz under which all Lyapunov exponents of a given linear cocycle are either positive or negative. As a consequence, we formulate new conditions for the existence of the so-called tempered exponential dichotomies. We consider cocycles over both maps and flows.

KEYWORDS:

• Linear cocycle
• Lyapunov exponents
• Rolewicz theorem
• tempered exponential dichotomies

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary: 37D25
• Secondary: 37H15
• 37A20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was partially supported by a Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) – Brazil postdoctoral fellowship [grant number 88881.120218/2016-01] at the University of Chicago. The second author was supported by the Hrvatska Zaklada za Znanost (Croatian Science Foundation) under the project IP-2014-09-2285 and by the University of Rijeka under the project number uniri-prirod-18-9.