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Denjoy-Wolff theorems for Hilbert’s and Thompson’s metric spaces

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Abstract

We study the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert’s metric or Thompson’s metric. We establish several Denjoy-Wolff type theorems which confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We also extend and put into a broader perspective results by Gaubert and Vigeral concerning the linear escape rate of such nonexpansive mappings.

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Author information

Authors and Affiliations

  1. University of Kent, Canterbury, Kent, CT2 7NX, UK

    Bas Lemmens

  2. Hampden-Sydney College, Hampden-Sydney, VA, 23943, USA

    Brian Lins

  3. Rutgers, The State University of New Jersey, Piscataway, NJ, 08854-8019, USA

    Roger Nussbaum

  4. North-West University, Private Bag X6001-209, Potchefstroom, 2520, South Africa

    Marten Wortel

Authors
  1. Bas Lemmens
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  2. Brian Lins
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  3. Roger Nussbaum
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  4. Marten Wortel
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Correspondence to Bas Lemmens.

Additional information

Supported by EPSRC grant EP/J008508/1.

Partially supported by NSFDMS 1201328.

Supported by EPSRC grant EP/J008508/1.

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Lemmens, B., Lins, B., Nussbaum, R. et al. Denjoy-Wolff theorems for Hilbert’s and Thompson’s metric spaces. JAMA 134, 671–718 (2018). https://doi.org/10.1007/s11854-018-0022-2

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  • DOI: https://doi.org/10.1007/s11854-018-0022-2

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