论文信息 - Numerical applications of equivariant reduction techniques

Numerical applications of equivariant reduction techniques

A new numerical method for detection and continuation of symmetry breaking bifurcation points is proposed. It avoids the construction of a symmetry adapted basis of the state space and the relevant block diagonalisation of the Jacobian. The method is related to the well-known techniques of augmented (bordered) Jacobians. The idea is to make a symmetry adapted choice of the bordering matrices which shoud induce a given representation of the symmetry group.

Vladimír Janovský | Petr Plecháč | P. Plecháč | V. Janovský

[1] Vladimír Janovský,et al. Computer-aided analysis of imperfect bifurcation diagrams, I. simple bifurcation point and isola formation centre. , 1992 .

[2] B. Werner,et al. Eigenvalue Problems with the Symmetry of a Group and Bifurcations , 1990 .

[3] A. Spence,et al. On a reduction process for nonlinear equations , 1989 .

[4] M. Golubitsky,et al. Singularities and groups in bifurcation theory , 1985 .

[5] E. Stiefel,et al. Gruppentheoretische Methoden und ihre Anwendung : eine Einführung mit typischen Beispielen aus Natur- und Ingenieurwissenschaften , 1979 .

[6] A. Spence,et al. Continuation and Bifurcations: Numerical Techniques and Applications , 1990 .

[7] M. Dellnitz,et al. Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points , 1989 .

[8] H. Mittelmann,et al. Numerical methods for bifurcation problems : proceedings of the conference at the University of Dortmund, August 22-26, 1983 , 1984 .

[9] Walter Knödel,et al. Graphentheoretische Methoden und ihre Anwendungen , 1969 .

[10] Asymptotic analysis of perturbed Takens-Bogdanov points , 1991 .

[11] A. Griewank,et al. Computation of cusp singularities for operator equations and their discretizations , 1989 .