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On the index of finite determinacy of vector fields with resonances

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Abstract

In this paper we study normal forms for a class of germs of 1-resonant vector fields on ℝn with mutually different eigenvalues which may admit extraneous resonance relations. We give an estimation on the index of finite determinacy from above as well as the essentially simplified polynomial normal forms for such vector fields. In the case that a vector field has a zero eigenvalue, the result leads to an interesting corollary, a linear dependence of the derivatives of the hyperbolic variables on the central variable.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Vincent Naudot

  2. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Jia Zhong Yang

Authors
  1. Vincent Naudot
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  2. Jia Zhong Yang
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Correspondence to Jia Zhong Yang.

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supported in part by NSFC-10571002

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Naudot, V., Yang, J.Z. On the index of finite determinacy of vector fields with resonances. Acta. Math. Sin.-English Ser. 24, 1401–1408 (2008). https://doi.org/10.1007/s10114-008-7073-8

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  • DOI: https://doi.org/10.1007/s10114-008-7073-8

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