Work

Generic Bifurcations of Symmetric Two-zone Piecewise Vector Fields on $$\mathbb {R}^3$$

Year: 2026

Type: article

Abstract: Inspired by Thom–Smale’s program on the qualitative classification of dynamical systems, we develop a structural framework for the local analysis of symmetric two-zone piecewise smooth vector fields on $$\mathbb {R}^3$$ R 3 . The framework is based on a natural correspondence with vector fields on manifolds with boundary, allowing local qualitative properties to be transferred to the symmetric piecewise setting. As applications, we derive complete classifications of generic codimension-zero and codimension-one R -reversible and R -equivariant symmetric singularities.

Source: Journal of Dynamics and Differential Equations

DOI: 10.1007/s10884-026-10537-8

Authors: U. Castro, J. Medrado

Institutions: Instituto Federal de Goiás, Instituto de Biociências, Letras e Ciências Exatas, câmpus de São José do Rio Preto, Universidade Estadual Paulista (Unesp)

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior