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Linear skew-product flows and semigroups of weighted composition operators

  • Chapter 1: Linear Random Dynamical Systems
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Lyapunov Exponents

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1486))

Abstract

The article contains the results on the relations between the spectral theory of linear skew-product flows, the multiplicative ergodic theorem and the spectral theory of the weighted composition operator semigroup. The latter is given by

$$(T_A^t f)(x) = \left( {\frac{{d\mu o \alpha ^{ - t} }}{{d\mu }}(x)} \right)^{{1 \mathord{\left/{\vphantom {1 2}} \right.\kern-\nulldelimiterspace} 2}} A(\alpha ^{ - t} x,t)f(\alpha ^{ - t} x),$$

acting in the space L 2(X, μ; H) of H-valued functions f on the compact space X; where A is a cocycle over the flow {αt} on X, t ∈ ℝ or ℤ.

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Author information

Authors and Affiliations

  1. Hydrophysics Institute, Ukrainian Academy of Science, Odessa, Russia

    Yu. D. Latushkin

  2. Moscow State University, Moscow, Russia

    A. M. Stepin

Authors
  1. Yu. D. Latushkin
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  2. A. M. Stepin
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Editor information

Ludwig Arnold Hans Crauel Jean-Pierre Eckmann

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© 1991 Springer-Verlag

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Latushkin, Y.D., Stepin, A.M. (1991). Linear skew-product flows and semigroups of weighted composition operators. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086661

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  • DOI: https://doi.org/10.1007/BFb0086661

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54662-7

  • Online ISBN: 978-3-540-46431-0

  • eBook Packages: Springer Book Archive

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