On commuting vector fields and Darboux functions for planar differential equations

A. Ghose Choudhury, Partha Guha

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We use Darboux polynomials to obtain an inverse integrating factor and present a method for determining commuting transversal systems for a planar ordinary differential system. We state a result of Garcia and Maza (J. Math. Anal. and Appl. 339 (2008) 740-745) that allows us to construct a linearization starting from a commutator. We illustrate its applicability with two examples. We also construct the rational potential isochrones for planar Hamiltonian systems. In addition we consider the issues of isochronicity and commuting transversal systems from a Lagrangian perspective.

Original languageBritish English
Pages (from-to)212-226
Number of pages15
JournalLobachevskii Journal of Mathematics
Volume34
Issue number3
DOIs
StatePublished - Jul 2013

Keywords

  • Darboux polynomials
  • Isochronicity
  • Linearizability
  • Transversal commuting systems

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