Number of invariant straight lines for homogeneous polynomial vector fields of arbitrary degree and dimension

Jaume Llibre, Violetta Pilyugina

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

We study the number of invariant straight lines through the origin of the homogeneous polynomial differential systems of degree m in ℝd or ℂd, when this number is finite. This notion extends in the natural way the classical notion of eigenvectors of homogeneous linear differential systems to homogeneous polynomial differential systems. This number provides un upper bound for the number of infinite singular points of the polynomial differential systems of degree m in. This upper bound is reached if all the invariant straight lines through the origin are real. © Springer Science+Business Media, LLC 2009.
Original languageEnglish
Pages (from-to)487-499
JournalJournal of Dynamics and Differential Equations
Volume21
DOIs
Publication statusPublished - 1 Aug 2009

Keywords

  • Homogeneous polynomial vector field
  • Infinite singular point
  • Invariant straight line
  • Polynomial vector field

Fingerprint

Dive into the research topics of 'Number of invariant straight lines for homogeneous polynomial vector fields of arbitrary degree and dimension'. Together they form a unique fingerprint.

Cite this