Conley-Morse databases for the angular dynamics of Newton's method on the plane

Justin Bush, Wes Cowan, Shaun Harker, Konstantin Mischaikow

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper we showcase the technique of Conley-Morse databases for studying a parameterized family of dynamical systems. The dynamical system of interest arises from considering the limiting behavior of Newton's root-finding method applied to functions f: ℝ2 → ℝ2 when the iterates converge to the origin. Considering the progression of angular orientations gives rise to a selfmap of the unit circle we call the angular dynamics map. We demonstrate how the technique of Conley-Morse dynamical databases allows us to quickly survey and prove theorems about the global dynamics of the parameterized family of angular dynamics maps.

Original languageEnglish (US)
Pages (from-to)736-766
Number of pages31
JournalSIAM Journal on Applied Dynamical Systems
Volume15
Issue number2
DOIs
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation

Keywords

  • Computational dynamics
  • Conley index
  • Conley-Morse databases
  • Global dynamics
  • Morse theory
  • Multiparameter dynamical systems
  • Newton's method

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