Polynomial dynamical systems and ordinary differential equations associated with the heat equation

V. M. Buchstaber, E. Yu Bunkova

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We consider homogeneous polynomial dynamical systems in n-space. To any such system our construction matches a nonlinear ordinary differential equation and an algorithm for constructing a solution of the heat equation. The classical solution given by the Gaussian function corresponds to the case n = 0, while solutions defined by the elliptic theta-function lead to the Chazy-3 equation and correspond to the case n = 2. We explicitly describe the family of ordinary differential equations arising in our approach and its relationship with the wide-known Darboux-Halphen quadratic dynamical systems and their generalizations.

Original languageEnglish
Pages (from-to)173-190
Number of pages18
JournalFunctional Analysis and its Applications
Volume46
Issue number3
DOIs
Publication statusPublished - Sep 2012
Externally publishedYes

Keywords

  • Chazy equation
  • Darboux-Halphen system
  • heat equation
  • polynomial dynamical systems

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