Vector fields on manifolds with boundary and reversibility -- An expository account

DOI10.1007/BF02970863zbMath1078.34026OpenAlexW2073229948MaRDI QIDQ1773861

Ronaldo A. Garcia, Marco Antonio Teixeira

Publication date: 3 May 2005

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02970863

zbMATH Keywords

ordinary differential equationsnonlinear dynamicsbifurcationsqualitative methodssingularities on a boundary

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) Dynamics induced by flows and semiflows (37C10) Singularities of vector fields, topological aspects (58K45) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations (34-01) Generic properties, structural stability of dynamical systems (37C20) Ordinary differential equations and systems on manifolds (34C40)

Cites Work

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• Structural stability on two-dimensional manifolds
• Time-reversal symmetry in dynamical systems: a survey
• Reversible systems
• Dynamical systems V. Bifurcation theory and catastrophe theory. Transl. from the Russian by N. D. Kazarinoff
• Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals
• Generic bifurcation in manifolds with boundary
• Qualitative theory of flows on surfaces (a review)
• Singularities of reversible vector fields
• Generic bifurcation of reversible vector fields on a 2-dimensional manifold
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Generic one-parameter families of vector fields on two-dimensional manifolds
• On the \(C^r\)-closing lemma
• Hopf-zero bifurcations of reversible vector fields
• Stability and regularity in bifurcations of planar vector fields
• Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
• An Improved Closing Lemma and a General Density Theorem

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