\(C^ p\) singularity theory and heteroclinic bifurcation with a distinguished parameter

DOI10.1016/0022-0396(92)90025-IzbMath0762.34021MaRDI QIDQ1198961

Stephen Schecter

Publication date: 16 January 1993

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

normal formsphase portraitsheteroclinic orbitbifurcation diagramsheteroclinic bifurcationsplanar dynamical systemshock solutionsuniversal unfoldings\(C^ p\) singularity theoryrecognition criteriasystem of two conservation laws in one space dimension

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Normal forms for dynamical systems (37G05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Local and nonlocal bifurcation theory for dynamical systems (37G99)

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Cites Work

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• Singularities and groups in bifurcation theory. Volume I
• Undercompressive shocks for nonstrictly hyperbolic conservation laws
• Singularities and groups in bifurcation theory. Volume II
• Simultaneous equilibrium and heteroclinic bifurcation of planar vector fields via the Melnikov integral