ENGLISH

Power geometry in algebraic and differential equations

By A.D. Bruno

Book information

Publisher
Elsevier
Year
2000
ISBN
0444502971, 9780444502971, 9780080539331
LCC
QA474 .B7513 2000
Open Library ID
OL18318325M
Language
english
Format
DJVU
Filesize
2 MB (2290557 bytes)
Series
North-Holland mathematical library 57
Edition
1st ed
Pages
397\397
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

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.

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