Stability of equivariant bifurcation problems with two types of state variables and their unfoldings in presence of parameter symmetry

doi:10.1007/s10483-007-0211-x

Applied Mathematics and Mechanics (English Edition) ›› 2007, Vol. 28 ›› Issue (2): 229-235 .doi: https://doi.org/10.1007/s10483-007-0211-x

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Stability of equivariant bifurcation problems with two types of state variables and their unfoldings in presence of parameter symmetry

CUI Deng-lan, LI Yang-cheng

1. School of Mathematical Science and Computing Technology, Central South University,Changsha 410083, P. R. China;
2. College of Mathematics and Computer Science, Hunan Normal University Changsha 410081, P. R. China

Received:2006-06-08 Revised:2006-11-13 Online:2007-02-18 Published:2007-02-18
Contact: CUI Deng-lan

Abstract

Abstract: Based on the contact equivalent elation of smooth map-germs in singularity theory, the stability of quivariant bifurcation problems with two types of state variables nd their unfoldings in the presence of parameter symmetry is iscussed. Some basic results are obtained. Transversality condition s used to characterize the stability of equavariant bifurcation roblems.

Key words: equivariant bifurcation problem, unfolding, k-stability, k-infinitesimal stability

2010 MSC Number:

CUI Deng-lan;LI Yang-cheng. Stability of equivariant bifurcation problems with two types of state variables and their unfoldings in presence of parameter symmetry. Applied Mathematics and Mechanics (English Edition), 2007, 28(2): 229-235 .

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Stability of equivariant bifurcation problems with two types of state variables and their unfoldings in presence of parameter symmetry

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