Barbashin-type conditions for exponential stability of linear cocycles


We formulate new conditions of Barbashin type for exponential stability of linear cocycles on arbitrary Banach spaces. We consider both cocycles over maps and flows. Our arguments rely on ergodic theory.

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I would like to thank the anonymous referees for their constructive comments that helped me to correct some inaccuracies in the first version of the paper.

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Correspondence to Davor Dragičević.

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Davor Dragičević was supported in part by Croatian Science Foundation under the Project IP-2019-04-1239 and by the University of Rijeka under the Projects uniri-prirod-18-9 and uniri-prprirod-19-16,

Communicated by H. Bruin.

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Dragičević, D. Barbashin-type conditions for exponential stability of linear cocycles. Monatsh Math (2020).

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  • Cocycle
  • Lyapunov exponents
  • Barbashin-type theorem

Mathematics Subject Classification

  • Primary 34D20
  • 34D08