Power geometry in algebraic and differential equations [EBook] / Alexander D. Bruno.
Power geometry in algebraic and differential equations [EBook] / Alexander D. Bruno.
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 d...
Personal Name(s):  Briuno, Aleksandr Dmitrievich. 

Edition: 
1st ed. 
Imprint: 
Amsterdam ; New York :
Elsevier,
2000

Physical Description: 
1 online resource (ix, 385 p.) : ill. 
Note: 
englisch 
ISBN: 
0080539335 9780080539331 0444502971 9780444502971 
Series Title: 
NorthHolland mathematical library ;
v. 57 
Subject (LOC):  
Full Text 
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. 