Power Geometry in Algebraic and Differential Equations

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.Power Geometry in Algebraic and Differential Equations is written by Bruno, A.D. and published by Elsevier Science. ISBNs for Power Geometry in Algebraic and Differential Equations are 9780444502971, 9780080539331, 0080539335 and the print ISBNs are 9780444502971, 0444502971.