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

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Feigenbaum, Mitchell J. — Quantitative universality for a class of nonlinear transformations
Feigenbaum, Mitchell J. — Quantitative universality for a class of nonlinear transformations

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Quantitative universality for a class of nonlinear transformations

Автор: Feigenbaum, Mitchell J.

Аннотация:

A large class of recursion relations x n + 1 = λ f(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximumbar x. Withf(bar x) - f(x) ˜ | {x - bar x} |^z (for| {x - bar x} | sufficiently small), z > 1, the universal details depend only upon z. In particular, the local structure of high-order stability sets is shown to approach universality, rescaling in successive bifurcations, asymptotically by the ratio α (α = 2.5029078750957... for z = 2). This structure is determined by a universal function g *( x), where the 2nth iterate of f, f (n), converges locally to α -n g *( α n x) for large n. For the class of f's considered, there exists a λ n such that a 2n-point stable limit cycle includingbar x exists; λ ∞ - λ n R δ -n ( δ = 4.669201609103... for z = 2). The numbers α and δ have been computationally determined for a range of z through their definitions, for a variety of f's for each z. We present a recursive mechanism that explains these results by determining g * as the fixed-point (function) of a transformation on the class of f's. At present our treatment is heuristic. In a sequel, an exact theory is formulated and specific problems of rigor isolated.


Язык: en

Рубрика: Физика/

Тип: Статья

Статус предметного указателя: Неизвестно

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 27

Добавлена в каталог: 08.04.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте