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Extended Holonomy and Topological Invariance of Vanishing Holonomy Group

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Abstract

In this work, we introduce the notion of extended holonomy and discuss some of its properties. As an application of it, we consider vanishing projective holonomy groups of germs of vector fields with zero (n − 1)-jet and prove, under some genericity assumptions, that the corresponding vanishing holonomy groups are topologically conjugated for orbitally topologically equivalent germs of vector fields.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México Area de la investigación científica, Ciudad Universitaria, C.P. 04510, México City, México

    L. Ortiz-Bobadilla & E. Rosales-González

  2. Departament of Mathematics, Chelyabinsk State University, Kashirin’s str. 129, Chelyabinsk, Russia, 454021

    S. M. Voronin

Authors
  1. L. Ortiz-Bobadilla
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  2. E. Rosales-González
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  3. S. M. Voronin
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Corresponding author

Correspondence to L. Ortiz-Bobadilla.

Additional information

This work was supported by the grants NCNIL_a 05-01-02801, RFBR 7-01-00017-a, and CONACyT 14300, PAPIIT-UNAM IN114703-3, IN102407.

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Ortiz-Bobadilla, L., Rosales-González, E. & Voronin, S.M. Extended Holonomy and Topological Invariance of Vanishing Holonomy Group. J Dyn Control Syst 14, 299–358 (2008). https://doi.org/10.1007/s10883-008-9041-0

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  • DOI: https://doi.org/10.1007/s10883-008-9041-0

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