Power Geometry in Algebraic and Differential Equations
( Volume 57 )
Publication series ：Volume 57
Publisher： Elsevier Science
Publication year： 2000
E-ISBN: 9780080539331
P-ISBN(Paperback): 9780444502971
P-ISBN(Hardback): 9780444502971
Subject： O123.1 plane geometry
Language： ENG
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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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