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An Example of Uniformly Recurrent Function which is not Almost Periodic

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Abstract

It is well-known that any almost periodic function is uniformly recurrent. We construct two examples which clarify the relations between these properties. The first one is an example of uniformly recurrent function which is unbounded. The second one is a bounded uniformly recurrent function, which is not almost periodic, even asymptotically.

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Université P. et M. Curie, Tour 55-65, 5ème étage, 4 pl. Jussieu, 75252 Paris cedex 05, France

    Alain Haraux

  2. Laboratoire de Mathématiques Appliquées, Université de Versailles, 45 av. des États Unis, 78035 Versailles cedex, France, and Département de Mathématiques, INSSET, Université de Picardie, 02109 St-Quentin, France

    Philippe Souplet

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  1. Alain Haraux
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  2. Philippe Souplet
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Correspondence to Alain Haraux or Philippe Souplet.

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Haraux, A., Souplet, P. An Example of Uniformly Recurrent Function which is not Almost Periodic. J. Fourier Anal. Appl. 10, 217–220 (2004). https://doi.org/10.1007/s00041-004-8012-4

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  • DOI: https://doi.org/10.1007/s00041-004-8012-4

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