Edited by
A.D. Bruno, Keldysh Institute of Applied Mathematics, RAS, Miusskaja sq.4, Moscow 125047, Russia
Description
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.
Included in series
North-Holland Mathematical Library
