Power geometry in algebraic and differential equations /
, Stepennai︠a︡ geometrii︠a︡ v algebraicheskikh i different︠s︡ialʹnykh uravnenii︠a︡kh. Collection : North-Holland mathematical library ; . v. 57 Mention d'édition :1st ed. Détails physiques : 1 online resource (ix, 385 pages) : illustrations. ISBN :9780444502971; 0444502971; 9780080539331 (electronic bk.); 0080539335 (electronic bk.).
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.
Preface. Introduction. The linear inequalitites. Singularities of algebraic equations. Hamiltonian truncations. Local analysis of an ODE system. Systems of arbitrary equations. Self-similar solutions. On complexity of problems of Power Geometry. Bibliography. Subject index.
Includes bibliographical references (p. 359-381) and index.
Description based on print version record.
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