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On Conformal Measures and Harmonic Functions for Group Extensions

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New Trends in One-Dimensional Dynamics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 285))

Abstract

We prove a Perron-Frobenius-Ruelle theorem for group extensions of topological Markov chains based on a construction of \(\sigma \)-finite conformal measures and give applications to the construction of harmonic functions.

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Acknowledgements

The author acknowledges support by CNPq through PQ 310883/2015-6 and Projeto Universal 426814/2016-9.

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Authors and Affiliations

  1. Universidade Federal do Rio de Janeiro-UFRJ, Rio de Janeiro, Brazil

    Manuel Stadlbauer

Authors
  1. Manuel Stadlbauer
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Correspondence to Manuel Stadlbauer .

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Editors and Affiliations

  1. Federal University of Rio de Janeiro IM-UFRJ, Institute of Mathematics, Rio de Janeiro, Brazil

    Maria José Pacifico

  2. Institute of Mathematics and Statistics, Fluminense Federal University, Niterói, Rio de Janeiro, Brazil

    Pablo Guarino

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Stadlbauer, M. (2019). On Conformal Measures and Harmonic Functions for Group Extensions. In: Pacifico, M., Guarino, P. (eds) New Trends in One-Dimensional Dynamics. Springer Proceedings in Mathematics & Statistics, vol 285. Springer, Cham. https://doi.org/10.1007/978-3-030-16833-9_15

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