# Power Geometry in Algebraic and Differential Equations, Volume 57

## 1st Edition

**Editors:**A.D. Bruno

**Hardcover ISBN:**9780444502971

**eBook ISBN:**9780080539331

**Imprint:**Elsevier Science

**Published Date:**1st June 2000

**Page Count:**396

**View all volumes in this series:**North-Holland Mathematical Library

## Table of Contents

## 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.

## Details

- No. of pages:
- 396

- Language:
- English

- Copyright:
- © Elsevier Science 2000

- Published:
- 1st June 2000

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9780080539331

- Hardcover ISBN:
- 9780444502971

## Reviews

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.

## About the Editors

### A.D. Bruno Editor

### Affiliations and Expertise

Keldysh Institute of Applied Mathematics, RAS, Miusskaja sq.4, Moscow 125047, Russia