On families of trajectories of an analytic gradient vector field

Volume 87 / 2005

Adam Dzedzej, Zbigniew Szafraniec Annales Polonici Mathematici 87 (2005), 99-109 MSC: Primary 37B35, 58K05; Secondary 14B05, 34C08. DOI: 10.4064/ap87-0-9

Abstract

For an analytic function $f:\mathbb R^n,0 \rightarrow \Bbb R,0$ having a critical point at the origin, we describe the topological properties of the partition of the family of trajectories of the gradient equation $\dot{x}=\nabla f(x)$ attracted by the origin, given by characteristic exponents and asymptotic critical values.

Authors

  • Adam DzedzejInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland
    e-mail
  • Zbigniew SzafraniecInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland
    e-mail

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