Asymptotic Rules of Equilibrium Desingularization

Yakov Krasnov, Iris Rabinowitz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A local bifurcation analysis of a high-dimensional dynamical system (Formula presented.) is performed using a good deformation of the polynomial mapping (Formula presented.). This theory is used to construct geometric aspects of the resolution of multiple zeros of the polynomial vector field (Formula presented.). Asymptotic bifurcation rules are derived from Grothendieck’s theory of residuals. Following the Coxeter–Dynkin classification, the singularity graph is constructed. A detailed study of three types of multidimensional mappings with a large symmetry group has been carried out, namely: 1. A linear singularity (behaves similarly to a one-dimensional complex analysis theory); 2. The lattice singularity (generalized the linear and resembling regular crystal growth models); 3. The fan-shaped singularity (can be split radially like nuclear fission and fusion models).

Original languageEnglish
Article number2186
JournalSymmetry
Volume14
Issue number10
DOIs
StatePublished - Oct 2022

Bibliographical note

Publisher Copyright:
© 2022 by the authors.

Keywords

  • bifurcation
  • phase portrait
  • polynomial differential systems
  • topological equivalence

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