A generalization of Gröbner bases helps to compute singularity theory transformations

DOI10.1002/zamm.20010811590zbMath0985.65158OpenAlexW1973708805MaRDI QIDQ2746090

Gerton Lunter

Publication date: 3 June 2002

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.20010811590

zbMATH Keywords

dynamical systemsGröbner basesHamiltonianbifurcation curvesdivision algorithmNewton's root-finding algorithmsingularity theory transformations

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical bifurcation problems (65P30) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Cites Work

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• Stability and Buchberger criterion for standard bases in power series rings
• Standard bases and some computations in rings of power series
• Equivariant singularity theory with distinguished parameters: two case studies of resonant Hamiltonian systems
• On the versal deformation of a complex space with an isolated singularity
• Resonances in a spring-pendulum: algorithms for equivariant singularity theory
• Birkhoff's normalization
• Computational methods of commutative algebra and algebraic geometry. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman

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