Power Geometry In Algebraic And Differential Equations

Download or read book Power Geometry in Algebraic and Differential Equations written by A.D. Bruno and published by Elsevier. This book was released on 2000-08-03 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.