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Detection of Special Curves Via the Double Resultant

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Abstract

We introduce several applications of the use of the double resultant through some examples of computation of different nature: special level sets of rational first integrals for rational discrete dynamical systems; remarkable values of rational first integrals of polynomial vector fields; bifurcation values in phase portraits of polynomial vector fields; and the different topologies of the offset of curves.

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Authors and Affiliations

  1. Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC) and Departament de Matemàtiques, Universitat Jaume I, Edifici TI (ESTEC), Av. de Vicent Sos Baynat, s/n, Campus del Riu Sec, 12071, Castelló de la Plana, Spain

    Antoni Ferragut

  2. Instituto de Matemática y Física, Universidad de Talca, Camino Lircay S/N, Campus Norte, Talca, Chile

    Johanna D. García-Saldaña

  3. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Armengol Gasull

Authors
  1. Antoni Ferragut
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  2. Johanna D. García-Saldaña
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  3. Armengol Gasull
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Corresponding author

Correspondence to Antoni Ferragut.

Additional information

The authors are partially supported by MINECO/ FEDER MTM2013-40998-P Grant. Johanna D. García-Saldaña is also partially supported by FONDECyT postdoctoral fellowship 3150131/2015. Armengol Gasull is also partially supported by Generalitat de Catalunya Grant 2014SGR568.

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Ferragut, A., García-Saldaña, J.D. & Gasull, A. Detection of Special Curves Via the Double Resultant. Qual. Theory Dyn. Syst. 16, 101–117 (2017). https://doi.org/10.1007/s12346-015-0180-x

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  • DOI: https://doi.org/10.1007/s12346-015-0180-x

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