Descripción del título
Power geometry in algebraic...
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
Monografía
monografia Rebiun03550321 https://catalogo.rebiun.org/rebiun/record/Rebiun03550321 m d |acr nuu---uuuuu 070802s2000 ne a sb 001 0 eng d 9780444502971 0444502971 UR0269109 OPELS. OPELS. BUS eng 516.22 22 Brëiìuno, Aleksandr Dmitrievich Stepennaëiìa geometriëiìa v algebraicheskikh i differenëtìsialnykh uravneniëiìakh. English Power geometry in algebraic and differential equations Recurso electrónico] Alexander D. Bruno 1st ed Servicio en línea Amsterdam New York Elsevier 2000 Amsterdam New York Amsterdam New York Elsevier ix, 385 p. ill. 23 cm ix, 385 p. North-Holland mathematical library v. 57 Libros electrónicos descargables Includes bibliographical references (p. 359-381) and index 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 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 ScienceDirect e-Books (Servicio en línea)