Power geometry in algebraic and differential equations [E-Book] / 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...
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Full text |
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Personal Name(s): | Briuno, Aleksandr Dmitrievich. |
Edition: |
1st ed. |
Imprint: |
Amsterdam ; New York :
Elsevier,
2000
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Physical Description: |
1 online resource (ix, 385 p.) : ill. |
Note: |
englisch |
ISBN: |
0080539335 9780080539331 0444502971 9780444502971 |
Series Title: |
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North-Holland mathematical library ;
v. 57 |
Subject (LOC): |
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. |