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Power geometry in algebraic and differential equations /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Amsterdam ; New York :
Elsevier,
2000.
|
| Edición: | 1st ed. |
| Colección: | North-Holland mathematical library ;
v. 57. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
MARC
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| 100 | 1 | |a Br�i�uno, Aleksandr Dmitrievich. | |
| 240 | 1 | 0 | |a Stepenna�i�a geometri�i�a v algebraicheskikh i differen�t�sial�nykh uravneni�i�akh. |l English |
| 245 | 1 | 0 | |a Power geometry in algebraic and differential equations / |c Alexander D. Bruno. |
| 250 | |a 1st ed. | ||
| 260 | |a Amsterdam ; |a New York : |b Elsevier, |c 2000. | ||
| 300 | |a 1 online resource (ix, 385 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a North-Holland mathematical library ; |v v. 57 | |
| 520 | |a 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. | ||
| 505 | 0 | |a 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. | |
| 504 | |a Includes bibliographical references (pages 359-381) and index. | ||
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 650 | 0 | |a Geometry, Plane. | |
| 650 | 0 | |a Differential-algebraic equations. | |
| 650 | 6 | |a G�eom�etrie plane. |0 (CaQQLa)201-0005153 | |
| 650 | 6 | |a �Equations diff�erentielles alg�ebriques. |0 (CaQQLa)201-0203503 | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a Differential-algebraic equations |2 fast |0 (OCoLC)fst00893501 | |
| 650 | 7 | |a Geometry, Plane |2 fast |0 (OCoLC)fst00940930 | |
| 776 | 0 | 8 | |i Print version: |a Br�i�uno, Aleksandr Dmitrievich. |s Stepenna�i�a geometri�i�a v algebraicheskikh i differen�t�sial�nykh uravneni�i�akh. English. |t Power geometry in algebraic and differential equations. |b 1st ed. |d Amsterdam ; New York : Elsevier, 2000 |z 0444502971 |z 9780444502971 |w (DLC) 00041723 |w (OCoLC)45029927 |
| 830 | 0 | |a North-Holland mathematical library ; |v v. 57. | |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780444502971 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/publication?issn=09246509&volume=57 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/bookseries/09246509/57 |z Texto completo |
| 880 | 8 | |6 505-00/(S |a 4. Truncated systems5. The power asymptotics; 6. Logarithmic asymptotics; 7. The simplex systems; 8. A big example; 9. Remarks; Chapter 4. Hamiltonian truncations; 1. The theory; 2. The generalized Henon-Heiles system; 3. The Sokol'skii cases of zero frequencies; 4. The restricted three-body problem; Chapter 5. Local analysis of an ODE system; 1. Introduction; 2. Normal form of a linear system; 3. The Newton polyhedron; 4. The reduction of System (3.10); 5. The classification of System (4.2); 6. The normal form of a nonlinear system; 7. Cases I and γ1; 8. System (4.2) in Cases II and IV | |
| 880 | 8 | |6 505-00/(S |a 9. The non-resonant case III10. The normal form in the resonant Case III; 11. The resonances of higher order; 12. The resonance 1:3 in Case III; 13. The resonance 1:2 in Case III; 14. The normal form in Case γ2; 15. The normal form in Cases γ0 and γ3; 16. The review of the results for System (4.2); 17. The transference of results to the original system; 18. The comparison with the Hamiltonian normal form; 19. The case μ=0; 20. The Belitskii normal form; 21. The problem of surface waves; 22. On the supernormal form; Chapter 6. Systems of arbitrary equations; 1. Truncated systems | |