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Genus for knots and links in renormalizable templates with several branch nodes

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Abstract

We apply kneading theory to describe the knots and links generated by the iteration of renormalizable nonautonomous dynamical systems with reducible kneading invariants, in terms of the links corresponding to each factor. As a consequence we obtain explicit formulas for the genus for this kind of knots and links.

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Acknowledgments

Luís Silva and Nuno Franco were partially supported by FCT-Portugal.

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Authors and Affiliations

  1. Department of Mathematics, University of Évora, Rua Romão Ramalho, 59, 700-671 , Évora, Portugal

    Pedro Simões

  2. CIMA-UE and Department of Mathematics, ISEL - Lisbon Superior Engineering Institute, Rua Conselheiro Emdio Navarro, 1, 1959 007 , Lisboa, Portugal

    Luís Silva

  3. CIMA-UE and Department of Mathematics, University of Évora, Rua Romão Ramalho, 59, 700-671 , Évora, Portugal

    Nuno Franco

Authors
  1. Pedro Simões
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  2. Luís Silva
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  3. Nuno Franco
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Correspondence to Luís Silva.

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Simões, P., Silva, L. & Franco, N. Genus for knots and links in renormalizable templates with several branch nodes. Nonlinear Dyn 77, 1035–1045 (2014). https://doi.org/10.1007/s11071-014-1361-x

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  • DOI: https://doi.org/10.1007/s11071-014-1361-x

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