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Ergodic solenoids and generalized currents

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Abstract

We introduce the concept of solenoid as an abstract laminated space. We do a thorough study of solenoids, leading to the notion of ergodic and uniquely ergodic solenoids. We define generalized currents associated with immersions of oriented solenoids endowed with a transversal measure into smooth manifolds, generalizing Ruelle-Sullivan currents.

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040, Madrid, Spain

    Vicente Muñoz

  2. CNRS, LAGA UMR 7539, Université Paris XIII, 99, Avenue J.-B. Clément, 93430, Villetaneuse, France

    Ricardo Pérez Marco

Authors
  1. Vicente Muñoz
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  2. Ricardo Pérez Marco
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Corresponding author

Correspondence to Vicente Muñoz.

Additional information

Research partially supported through Spanish MEC grant MTM2007-63582. Second author supported by CNRS (UMR 7539).

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Muñoz, V., Pérez Marco, R. Ergodic solenoids and generalized currents. Rev Mat Complut 24, 493–525 (2011). https://doi.org/10.1007/s13163-010-0050-7

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  • DOI: https://doi.org/10.1007/s13163-010-0050-7

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