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Topological classification of linear hyperbolic cocycles

  • Nguyen Dinh Cong
Article

Abstract

In this paper linear hyperbolic cocycles are classified by the relation of topological conjugacy. Roughly speaking, two linear cocycles are conjugate if there exists a homeomorphism which maps their trajectories into each other. The problem of classification of discrete-time deterministic hyperbolic dynamical systems was investigated by Robbin (1972). He proved that there exist 4d classes ofd-dimensional deterministic discrete hyperbolic dynamical systems. We obtain a criterion for topological conjugacy of two linear hyperbolic cocycles and show that the number of classes depends crucially on the ergodic properties of the metric dynamical system over which they are defined. Our result is a generalization of the deterministic theorem of Robbin.

Key words

Linear hyperbolic cocycle random homeomorphism Oseledets splitting orientation dimension coboundary 

AMS Subject Classification

S8F15 28D05 58F19 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Nguyen Dinh Cong
    • 1
    • 2
  1. 1.Institut für Dynamische SystemeUniversität BremenBremenGermany
  2. 2.Hanoi Institute of MathematicsHanoiVietnam

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