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Fixed Points of Composition Operators

  • Chapter
Nonlinear Evolution and Chaotic Phenomena

Part of the book series: NATO ASI Series ((NSSB,volume 176))

Abstract

These lectures will be concerned with the following problem:

Let v be fixed in [1, 2]. Find real constants λ ∈ (0, 1) and r > 1, and a solution ∅ of the functional equation

$$ phi (x) = - \frac{1}{\lambda }\phi \left( {\frac{1}{{\lambda ^{v - 1} }}\phi (\lambda ^v x)} \right),\;\phi (0) = 1, $$
(1.1)

with the properties C1,C2 below, and a further property C3 to be stated later C1. φ is C1 and strictly decreasing on [0, L] for some L ≥ 1. For all x ∈ [0, L], φ (⋋v x) is in [0, ⋋v-1 L] and (1.1) holds.

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Author information

Authors and Affiliations

  1. CNRS and IHES, Bures sur Yvette, France

    Henri Epstein

Authors
  1. Henri Epstein
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Editor information

Editors and Affiliations

  1. Accademia dei Lincei, Centro Linceo Interdisciplinare “B. Segre”, Rome, Italy

    Giovanni Gallavotti

  2. Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

    Paul F. Zweifel

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© 1988 Plenum Press, New York

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Epstein, H. (1988). Fixed Points of Composition Operators. In: Gallavotti, G., Zweifel, P.F. (eds) Nonlinear Evolution and Chaotic Phenomena. NATO ASI Series, vol 176. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1017-4_6

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  • DOI: https://doi.org/10.1007/978-1-4613-1017-4_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8294-5

  • Online ISBN: 978-1-4613-1017-4

  • eBook Packages: Springer Book Archive

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