Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities

Jackson Itikawa, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

We classify the global phase portraits in the Poincaré disc of the differential systems x• = -y + xf(x; y); y• = x + yf(x; y), where f(x; y) is a ho-mogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. This paper together with the results presented in [9] com-pletes the classification of the global phase portraits in the Poincaré disc of all quartic polynomial differential systems with a uniform isochronous center at the origin.
Original languageEnglish
Pages (from-to)121-131
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume21
Issue number1
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • Disk
  • Phase portrait
  • Poincaré
  • Polynomial vector field
  • Quartic polynomial differential system
  • Uniform isochronous center

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