Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   

Поиск по указателям

Khovanskii A. — Fewnomials (Translations of Mathematical Monographs)
Khovanskii A. — Fewnomials (Translations of Mathematical Monographs)

Читать книгу

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Fewnomials (Translations of Mathematical Monographs)

Автор: Khovanskii A.


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.

Язык: en

Рубрика: Разное/

Статус предметного указателя: Неизвестно

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 151

Добавлена в каталог: 02.07.2016

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
Предметный указатель
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2019
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте