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Publications and Preprints by Karin Gatermann

M. Eiswirth, K. Gatermann, A. Sensse:

Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems.

Version of January 16. 2004: EiGaSe040116.ps.

K. Gatermann, Xia Bican:

Existence of 3 positive solutions of systems from chemistry.

Version of July 8. 2003: GaXia.ps .

K. Gatermann, M. Wolfrum:

Bernstein's second theorem and Viro's method for sparse polynomial systems in chemistry.

Version of Sept. 5. 2003: GaWol030905.ps .

To appear in Advances in Applied Mathematics.

K. Gatermann, P. Parrilo:

Symmetry groups, semidefinite programs, and sum of squares.

Journal of Pure and Applied Algebra, Vol. 192, p. 95-128, 2004.

SymmetricSOS.ps .

K. Gatermann, W. Koepf (Eds.):

Special Issue Computer Algebra and Computer Analysis.

Journal of Symbolic Computation 35 (5), 2003.

K. Gatermann:

Applications of SAGBI-bases in dynamics.

Journal of Symbolic Computation 35, 543-575, 2003.

gatesagbi2.ps .

K. Gatermann, S. Hosten:

Computational algebra for bifurcation theory.

Submitted to Journal of Symbolic Computation, special issue ACA 2002.

2002. GatHosbif.ps .

K. Gatermann:

Graph Theory Applications in Chemistry.

Invited article in Proceedings of EWM-workshop Groups and Graphs, Varna, Bulgaria, 2002.

K. Gatermann:

Counting stable solutions of sparse polynomial systems in chemistry.

Contemporary Math. Volume 286,

Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering,

Editors: E. Green, S. Hosten, R. Laubenbacher, V. Powers, 53--69, AMS, Providence, Rhode Island, 2001, final version .

K. Gatermann, B. Huber:

A family of sparse polynomial systems arising in chemical reaction systems.

Journal of Symbolic Computation 33(3), 275-305, 2002.

Version of October 1. 2000: JSCshort.ps .

K. Gatermann:

Computer Algebra methods for equivariant dynamical systems.

Habilitationsschrift FU Berlin, 1999.

Lecture Notes in Mathematics Volume 1728, Springer 2000.

A. Lari-Lavassani, W.F. Langford, K. Huseyin, K. Gatermann:

Steady-state mode interactions for D3 and D4-symmetric systems.

Dynamics of Continuous, Discrete and Impulsive Systems 6, 169--209, 1999.

(ps-file available here )

K. Gatermann, F. Guyard:

Gröbner bases, invariant theory and equivariant dynamics.

Journal of Symbolic Computation 28, p. 275--302, 1999. (ps-file available here )

K. Gatermann:

Testing for S_n-Symmetry with a Recursive Detective.

In: H.W. Broer, S.A. von Gils, I. Hoveijn, F. Takens (Eds.), Nonlinear Dynamical Systems and Chaos, 61-78, Birkhäuser, Basel, Boston, Berlin, 1996.

(SC 95-12, 1995).

K. Gatermann:

Semi-invariants, equivariants and algorithms. Appl. Algebra Eng. Comm. Comput. 7, 105-124, 1996. (ps-file available here )

K. Gatermann, R. Lauterbach:

Automatic classification of normal forms.

Nonlinear Analysis 34, 157-190, 1998. (ps-file available here )

J. Verschelde, K. Gatermann, R. Cools:

Mixed Volume Computation by Dynamic Lifting

applied to Polynomial System Solving.

Journal of Discrete & Computational Geometry 16, 69-112, 1996.

J. Verschelde, K. Gatermann:

Symmetric Newton Polytopes for Solving Sparse Polynomial Systems.

Adv. Appl. Math. 16 (1), 95-127, 1995.

(SC 94-3, 1994).

K. Gatermann, B. Werner,

Secondary Hopf Bifurcation Caused by Steady-state Steady-state Mode interaction. In J. Chaddam, M. Golubitsky, W. Langford, B. Wetton (Eds.), Pattern Formations: Symmetry Methods and Applications, p 209-224, Fields Institute Communications Volume 5, 1996.

(SC 93-16, 1993).

K. Gatermann:

A remark on the detection of symmetry of attractors.

In P. Chossat (Ed.), Dynamics, Bifurcation and Symmetry, New Trends and New Tools, pp. 123, Kluwer Academic Publishers, Dordrecht, 1994.

K. Gatermann, B. Werner:

Group Theoretical Mode Interactions with Different Symmetries. International Journal on Bifurcation and Chaos 4, 177-191, 1994.

(SC 93-3, 1993).

K. Gatermann:

Computation of Bifurcation Graphs. In: E. Allgower, K. Georg, R. Miranda (eds.), Exploiting Symmetry in Applied and Numerical Analysis: 1992 AMS-SIAM Summer Seminar in Applied Mathematics, July 26- August 1, 1992, AMS Lectures in Applied Mathematics V. 29, 187-201, Providence, Rhode Island, 1993.

(SC 92-13, 1992).

K. Gatermann:

Linear representations of finite groups and the ideal theoretical construction of G-invariant cubature formulas. In T.O. Espelid, A. Genz (eds.), Numerical Integration, 25-35, Kluwer Academic Publishers, 1992.

K. Gatermann, Ch. Hoffmann, G. Opfer:

Explicit Faber Polynomials on Circular Sectors. Math. Comp. 58 (197), 241-253, 1992.

K. Gatermann, A. Hohmann:

Hexagonal Lattice Dome - Illustration of a Nontrivial Bifurcation Problem. Konrad-Zuse-Zentrum, Preprint SC 91-8, 1991.

H. Caprasse, J. Demaret, K. Gatermann, H. Melenk:

Power-law type solutions of fouth-order gravity for multidimensional Bianchi I universes. Int. J. Mod. Phys. C. 2, No.2, 601-611, 1991.

(SC 90-18, 1990).

K. Gatermann:

Mixed symbolic-numeric solution of symmetrical nonlinear systems . In St. Watt (Ed.), Proceedings of ISSAC-91 (Bonn, Germany, July 15-17, 1991), 431-432, ACM, New York, 1991.

K. Gatermann, A. Hohmann:

Symbolic Exploitation of Symmetry in Numerical Pathfollowing. Impact of Computing in Science and Engineering 3, 330-365, 1991.

(SC 90-11, 1990).

K. Gatermann:

Symbolic solution of polynomial equation systems with symmetry.

In Sh. Watanabe, M. Nagata (Eds.), Proceedings of ISSAC--90 (Tokyo, Japan, August 20-24, 1990), 112-119. ACM, New York, 1990.

(SC 90-3, 1990).

K. Gatermann:

Gruppentheoretische Konstruktion von symmetrischen Kubaturformeln. Dissertation an der Universität, 1990.

(TR 90-1, 1990).

K. Gatermann:

The Construction of Symmetric Cubature Formulas for the Square and the Triangle. Computing 40, 229--240, 1988.