# Fewnomials / A. G. Khovanskii

Type de document : MonographieCollection : Translations of mathematical monographs, 88Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 1991Description : 1 vol. (VIII-139 p.) : appendix ; 26 cmISBN: 9780821845479.ISSN: 0065-9282.Bibliographie : Bibliogr.p. 133-136. Index.Sujet MSC : 12D10, Field theory and polynomials - Real and complex fields, Polynomials: location of zeros (algebraic theorems)32B20, Several complex variables and analytic spaces - Local analytic geometry, Semi-analytic sets, subanalytic sets, and generalizations

14P05, Algebraic geometry - Real algebraic and real analytic geometry, Real algebraic sets

14P15, Algebraic geometry - Real algebraic and real analytic geometry, Real-analytic and semi-analytic sets

58A17, Global analysis, analysis on manifolds - General theory of differentiable manifolds, Pfaffian systemsEn-ligne : Zentralblatt | MathSciNet | AMS

Item type | Current library | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|

Monographie | CMI Salle 1 | 12 KHO (Browse shelf(Opens below)) | Available | 11868-01 |

Bibliogr.p. 133-136. Index

The ideology of the theory of fewnomials is the following: real varieties defined by "simple," not cumbersome, systems of equations should have a "simple" topology. One of the results of the theory is a real transcendental analogue of the Bezout theorem: for a large class of systems of k transcendental equations in k real variables, the number of roots is finite and can be explicitly estimated from above via the "complexity" of the system. A more general result is the construction of a category of real transcendental manifolds that resemble algebraic varieties in their properties. These results give new information on level sets of elementary functions and even on algebraic equations.

The topology of geometric objects given via algebraic equations (real-algebraic curves, surfaces, singularities, etc.) quickly becomes more complicated as the degree of the equations increases. It turns out that the complexity of the topology depends not on the degree of the equations but only on the number of monomials appearing in them. This book provides a number of theorems estimating the complexity of the topology of geometric objects via the cumbersomeness of the defining equations. In addition, the author presents a version of the theory of fewnomials based on the model of a dynamical system in the plane. Pfaff equations and Pfaff manifolds are also studied. (source : AMS)

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