書誌事項

Fewnomials

A.G. Khovanskiĭ

(Translations of mathematical monographs, v. 88)

American Mathematical Society, c1991

タイトル別名

Малочлены

Malochleny

この図書・雑誌をさがす
注記

Includes index

Bibliography: p. 133-136

Translated from the Russian by Smilka Zdravkovska

内容説明・目次

内容説明

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 given 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.

目次

An Analogue of the Bezout Theorem for a System of Real Elementary Equations Two Simple Versions of the Theory of Fewnomials Analogues of the Theorems of Rolle and Bezout for Separating Solutions of Pfaff Equations Pfaff Manifolds Real-Analytic Varieties with Finiteness Properties and Complex Abelian Integrals.

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詳細情報
  • NII書誌ID(NCID)
    BA12622464
  • ISBN
    • 0821845470
  • LCCN
    91002504
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 原本言語コード
    rus
  • 出版地
    Providence, R.I.
  • ページ数/冊数
    viii, 139 p.
  • 大きさ
    27 cm
  • 分類
  • 件名
  • 親書誌ID
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