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Chaotic Orbits for Systems of Nonlocal Equations

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Abstract

We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinic, homoclinic and chaotic trajectories are constructed. This is the first attempt to consider a nonlocal version of this type of dynamical systems in a variational setting and the first result regarding symbolic dynamics in a fractional framework.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Melbourne, 813 Swanston St., Parkville, VIC, 3010, Australia

    Serena Dipierro & Enrico Valdinoci

  2. School of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, Perth, WA, 6009, Australia

    Serena Dipierro & Enrico Valdinoci

  3. Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Austin, TX, 78751, USA

    Stefania Patrizi

  4. Weierstraß Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, 10117, Berlin, Germany

    Enrico Valdinoci

  5. Dipartimento di Matematica, Università degli studi di Milano, Via Saldini 50, 20133, Milan, Italy

    Enrico Valdinoci

  6. Istituto di Matematica Applicata e Tecnologie Informatiche, Consiglio Nazionale delle Ricerche, Via Ferrata 1, 27100, Pavia, Italy

    Enrico Valdinoci

Authors
  1. Serena Dipierro
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  2. Stefania Patrizi
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  3. Enrico Valdinoci
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Correspondence to Stefania Patrizi.

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Communicated by C. Liverani

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Dipierro, S., Patrizi, S. & Valdinoci, E. Chaotic Orbits for Systems of Nonlocal Equations. Commun. Math. Phys. 349, 583–626 (2017). https://doi.org/10.1007/s00220-016-2713-9

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  • DOI: https://doi.org/10.1007/s00220-016-2713-9

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