Construction of Smooth Sphere Maps with Given Degree and a Generalization of Morse Index Formula for Smooth Vector Fields

• Xiao-Song Yang ^[1]
  1. [1] Huazhong University of Science and Technology

     Huazhong University of Science and Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 14, Nº 1, 2015, págs. 139-147
• Idioma: inglés
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• Resumen

  • This paper presents a fundamental lemma concerning the index of a zero of a vector field. Based on this lemma one obtains a procedure of constructing a higher dimensional smooth sphere map from a lower dimensional one and gives an explicit formula for smooth sphere map with a given topological degree. Also based on this lemma, a new proof of the generalized Morse index formula is presented for smooth vector fields on a manifold with boundary.