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Cantor Sets, Bernoulli Shifts and Linear Dynamics

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Descriptive Topology and Functional Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 80))

Abstract

Our purpose is to review some recent results on the interplay between the symbolic dynamics on Cantor sets and linear dynamics. More precisely, we will give some methods that allow the existence of strong mixing measures invariant for certain operators on Fréchet spaces, which are based on Bernoulli shifts on Cantor spaces. Also, concerning topological dynamics, we will show some consequences for the specification properties.

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Acknowledgments

This work is supported in part by MICINN and FEDER, Projects MTM2010-14909 and MTM2013-47093-P. The third author is supported by a grant from the FPU Program of MEC. The second and fourth authors were partially supported by GVA, Project PROMETEOII/2013/013.

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Authors and Affiliations

  1. IUMPA, Universitat Politècnica de València, 46022, Valencia, Spain

    Salud Bartoll, Félix Martínez-Giménez, Marina Murillo-Arcila & Alfredo Peris

Authors
  1. Salud Bartoll
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  2. Félix Martínez-Giménez
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  3. Marina Murillo-Arcila
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  4. Alfredo Peris
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Corresponding author

Correspondence to Alfredo Peris .

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Editors and Affiliations

  1. Center Operations Research Univ. Inst., Universidad Miguel Hernandez, Elche, Alicante, Spain

    Juan Carlos Ferrando

  2. Matematica Aplicada, Universidad Politecnica de Valencia, Valencia, Valencia, Spain

    Manuel López-Pellicer

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Bartoll, S., Martínez-Giménez, F., Murillo-Arcila, M., Peris, A. (2014). Cantor Sets, Bernoulli Shifts and Linear Dynamics. In: Ferrando, J., López-Pellicer, M. (eds) Descriptive Topology and Functional Analysis. Springer Proceedings in Mathematics & Statistics, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-319-05224-3_10

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