Bounded polynomial vector fields

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Abstract

We prove that, for generic bounded polynomial vector fields in Rn with isolated critical points, the sum of the indices at all their critical points is (−1)n. We characterize the local phase portrait of the isolated critical points at infinity for any bounded polynomial vector field in Rn. We apply this characterization to show that there are exactly seventeen different behaviours at infinity for bounded cubic polynomial vector fields in the plane. © 1990 American Mathematical Society.
Original languageEnglish
Pages (from-to)557-579
JournalTransactions of the American Mathematical Society
Volume318
Issue number2
DOIs
Publication statusPublished - 1 Jan 1990

Keywords

  • Blow-up
  • Bounded vector field
  • Index

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