Computational algebra for bifurcation theory

Journal of Symbolic Computation

Volumn 40, Issue 4-5 SPEC. ISS., 2005, Pages 1180-1207

  Gatermann, Karin ^a   Hosten, Serkan ^a,b  

^a ZUSE INSTITUTE BERLIN   (Germany)

^b SAN FRANCISCO STATE UNIVERSITY   (United States)

Author keywords

Bifurcation point; Local ring; Singularity theory; Standard bases

Indexed keywords

EID: 26944480391     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2004.04.007     Document Type: Article

References (24)

1. M.E. Alonso T. Mora M. Raimondo A computational model for algebraic power series Journal of Pure and Applied Algebra 92 1992 1-38
2. D. Armbruster Bifurcation theory and computer algebra: An initial approach In: B.F. Caviness (Ed.) Eurocal '85 1985 Springer Berlin 126-136
3. V.I. Arnold Dynamical Systems VI, Singularity Theory I In: Encyclopaedia of Mathematical Sciences vol. 6 1993 Springer Berlin
4. V.I. Arnold Dynamical Systems V, Bifurcation Theory and Catastrophe Theory In: Encyclopaedia of Mathematical Sciences vol. 5 1994 Springer Berlin
5. H. Broer I. Hoveijn G. Lunter G. Vegter Bifurcations in Hamiltonian Systems, Computing Singularities by Gröbner Bases In: Lecture Notes in Mathematics vol. 1806 2003 Springer Berlin
6. J. Calmet M. Hausdorf W. Seiler A constructive introduction to involution In: R. Akerkar (Ed.) Proc. Int. Symp. Applications of Computer Algebra - ISACA 2000 2001 Allied Publishers New Delhi 33-50
7. R.G. Cowell F.J. Wright CATFACT: Computer algebraic tools for applications to catastrophe theory In: J.H. Davenport (Ed.) EUROCAL'87 Europian Conference on Computer Algebra 2-5 June 1987, Leipzig In: Lecture Notes in Computer Science vol. 378 1987 Springer Berlin 71-80
8. D. Cox J. Little D. O'Shea Using Algebraic Geometry 1998 Springer Verlag New York
9. T. Gaffney New methods in the classification theory of bifurcation problems In: Contemporary Mathematics vol. 56 1986 American Mathematical Society 97-116
10. K. Gatermann R. Lauterbach Automatic classification of normal forms Nonlinear Analysis, Theory, Methods, and Applications 34 1998 157-190
11. R. Gebauer H.M. Möller On an installation of Buchberger's algorithm Journal of Symbolic Computation 6 1988 275-286
12. M. Golubitsky D.G. Schaeffer Singularities and Groups in Bifurcation Theory I In: Applied Mathematical Sciences vol. 51 1985 Springer New York
13. M. Golubitsky I. Stewart D.G. Schaeffer Singularities and Groups in Bifurcation Theory II In: Applied Mathematical Sciences vol. 69 1988 Springer New York
14. W.J.F. Govaerts Computation of singularities in large nonlinear systems SIAM Journal on Numerical Analysis 34 1997 867-880
15. W.J.F. Govaerts Numerical Methods for Bifurcations of Dynamical Equilibria 2000 SIAM Philadelphia
16. Grassmann, H., Greuel, G.-M., Martin, B., Neumann, W., Pfister, G., Pohl, W., Schönemann, H., Siebert, T., 1996. Standard bases, syzygies and their implementation in singular. In: Reports On Computer Algebra, number 01. Centre for Computer Algebra, University of Kaiserslautern, July 1996. Online available at http://www.mathematik.uni-kl.de/~zca
17. Greuel, G.-M., Pfister, G., Schönemann, H., 2001. Singular 2.0. A Computer Algebra System for Polynomial Computations, Centre for Computer Algebra, University of Kaiserslautern. http://www.singular.uni-kl.de
18. E. Hille Analytic Function Theory vol. II 1962 Ginn and Company Boston
19. H. Hironaka Resolution of singularities of an algebraic variety over a field of characteristic zero I, II. Ann. Math. 79 1964 109-203
20. Y.A. Kuznetsov Elements of Applied Bifurcation Theory In: Applied Mathematical Sciences vol. 112 1995 Springer New York
21. Z. Mei Numerical bifurcation analysis for reaction-diffusion equations In: Springer Series in Computational Mathematics vol. 28 2000 Springer Berlin
22. I. Melbourne The recognition problem for equivariant singularities Nonlinearity 1 1988 215-240
23. T. Mora An algorithm to compute the equations of tangent cones In: J. Calmet (Ed.) Computer Algebra, EUROCAM '82, European Computer Algebra Conference 5-7 April 1982, Marseille, France Lecture Notes in Computer Science vol. 144 1982 Springer 158-165
24. M.M Vainberg V.A. Trenogin Theory of Branching of Solutions of Non-linear Equations 1974 Noordhoff International Publishing Leyden (Translated by Israel Program. Original title Teoriya vetvleniya reshenii nelineinykh uravnenii published in 1969 in Moscow)