Normal Forms, Differentiable Conjugacies, and Elementary Bifurcations of Maps

DOI10.1137/22m1503701zbMath1521.37049arXiv2206.04840OpenAlexW4367307408MaRDI QIDQ6045345

David J. W. Simpson, Paul Glendinning

Publication date: 26 May 2023

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.04840

zbMATH Keywords

saddle-node bifurcationnormal formstranscritical bifurcationbifurcation theorypitchfork bifurcationperiod-doubling bifurcationdifferentiable conjugacy

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Bifurcations of singular points in dynamical systems (37G10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topological equivalences for one-parameter bifurcations of scalar maps
• Local \(C^n\) transformations of the real line
• Reducing conjugacy in the full diffeomorphism group of \(\mathbb R\) to conjugacy in the subgroup of orientation-preserving maps
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Smooth classification of one-dimensional diffeomorphisms with hyperbolic fixed points
• Normal forms for certain singularities of vectorfields
• Conjugacy of real diffeomorphisms. A survey
• Singularities, Bifurcations and Catastrophes
• Stability, Instability and Chaos
• $C^k$ conjugacy of 1-d diffeomorphisms with periodic points
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Smooth conjugacy of difference equations derived from elliptic curves
• Elements of applied bifurcation theory