Power Geometry in Algebraic and Differential Equations

by A.D. Bruno

Overview

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.

Product Details

ISBN-13:	9780444502971
Publisher:	Elsevier Science
Publication date:	08/03/2000
Series:	North-Holland Mathematical Library , #57
Pages:	396
Product dimensions:	0.94(w) x 6.14(h) x 9.21(d)

Table of Contents

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.