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Lyapunov functions versus exponential contractions

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Abstract

For nonautonomous linear equations in a Banach space admitting a nonuniform version of exponential contraction, we give an optimal characterization of the exponential behavior in terms of strict Lyapunov sequences. In particular, we construct explicitly strict Lyapunov sequences for each exponential contraction. We also consider the particular case of quadratic Lyapunov functions, and we use the corresponding characterization of the exponential behavior in terms of these functions to show that the stability of an exponential contraction persists under sufficiently small perturbations.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisbon, Portugal

    Luis Barreira & Claudia Valls

Authors
  1. Luis Barreira
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  2. Claudia Valls
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Correspondence to Luis Barreira.

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Partially supported by FCT through CAMGSD, Lisbon.

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Barreira, L., Valls, C. Lyapunov functions versus exponential contractions. Math. Z. 268, 187–196 (2011). https://doi.org/10.1007/s00209-010-0665-x

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  • DOI: https://doi.org/10.1007/s00209-010-0665-x

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