Power Geometry in Algebraic and Differential Equations

Erscheinungsjahr 2000
ISBN: 978-0-444-50297-1
Verlag: Elsevier Science & Technology

Buch, Englisch, 396 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 730 g

The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed.The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems.The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.

Autoren/Hrsg.

Bruno, A.D.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Preface. Introduction. The linear inequalitites. Singularities of algebraic equations. Hamiltonian truncations. Local analysis of an ODE system. Systems of arbitrary equations. Self-similar solutions. On complexity of problems of Power Geometry. Bibliography. Subject index.