Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 183-209

PERIODIC APPROXIMATION OF EXCEPTIONAL LYAPUNOV EXPONENTS FOR SEMI-INVERTIBLE OPERATOR COCYCLES

Lucas Backes and Davor Dragicevic

Universidade Federal do Rio Grande do Sul, Departamento de Matemática
Av. Bento Gonçalves 9500, CEP 91509-900, Porto Alegre, RS, Brazil; lhbackes 'at' impa.br

University of Rijeka, Department of Mathematics
51000 Rijeka, Croatia; ddragicevic@math.uniri.hr

Abstract. We prove that for semi-invertible and Hölder continuous linear cocycles A acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov closing property, all exceptional Lyapunov exponents of A with respect to an ergodic invariant measure for base dynamics can be approximated with Lyapunov exponents of A with respect to ergodic measures supported on periodic orbits. Our result is applicable to a wide class of infinite-dimensional dynamical systems.

2010 Mathematics Subject Classification: Primary 37H15, 37A20; Secondary 37D25.

Key words: Semi-invertible operator cocycles, Lyapunov exponents, periodic points, approximation.

Reference to this article: L. Backes and D. Dragicevic: Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles. Ann. Acad. Sci. Fenn. Math. 44 (2019), 183-209.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4410