𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Power geometry in algebraic and differential equations

✍ Scribed by A.D. Bruno

Book ID
127419773
Publisher
Elsevier
Year
2000
Tongue
English
Weight
2 MB
Series
North-Holland mathematical library 57
Edition
1st ed
Category
Library
City
Amsterdam; New York
ISBN
0080539335

No coin nor oath required. For personal study only.

✦ Synopsis

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.<br

πŸ“œ SIMILAR VOLUMES

Differential Equations and Algebraic Rel
Differential Equations and Algebraic Relations
✍ Elie Compoint πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 542 KB

We consider a linear differential equation Ly = 0 of order n with coefficients in C(z) whose differential Galois group G is supposed to be reductive and unimodular. We give an algorithm for the construction of a system of generators of the ideal of algebraic relations, with coefficients in C(z), amo