Keller K. — Invariant Factors, Julia Equivalences and the (Abstract)Mandelbrot Set :: Электронная библиотека попечительского совета мехмата МГУ

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Keller K. — Invariant Factors, Julia Equivalences and the (Abstract)Mandelbrot Set

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Название: Invariant Factors, Julia Equivalences and the (Abstract)Mandelbrot Set

Автор: Keller K.

Аннотация:

This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. The conceptual kernel is a self-contained abstract counterpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated in the complex plane. It is used to give rigorous proofs of some well-known and some partially new statements on the structure of the Mandelbrot set. The text is intended for graduate students and researchers. Some elementary knowledge in topology and in functions of one complex variable is assumed.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 205

Добавлена в каталог: 17.08.2008

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Предметный указатель

Point, periodic, irrationally indifferent      8
Point, periodic, non-primitive      145
Point, periodic, parabolic      8
Point, periodic, primitive      145
Point, periodic, repelling      8
Point, periodic, superattractive      8
Point, postcritical      8
Point, preperiodic      7
Polynomial, quadratic, infinitely renormalizable      14
Polynomial, quadratic, n-renormalizable      14
Preperiod      7
QML (quadratic minor lamination)      89
Ramification order of a point      71
Ray, dynamic      9
Ray, parameter      15
Renormalization of a quadratic polynomial      14
Renormalization of a quadratic polynomial, crossed      14
Renormalization of a quadratic polynomial, simple      14
Root, of a hyperbolic component      19
Root, of the critical value Fatou component      144
S | n (initial subword of length n of a sequence s)      25
S(n) (n-th symbol of a sequence s)      25
Semi-conjugacy      4
Semi-conjugate      4
Separate hyperbolic components      20
Sequence tuning      92
Sequence, $\alpha$ -regular      31
Sequence, n-renormalizable      107
Sequence, Sturmian      29 102

Set, f-invariant      49
Set, minimal      49
Set, self-similar      185
Shift map      6 25
Siegel disk      142
Siegel point      142
Sierpinski triangle      186
STEP, of a boundary chord      123
STEP, of a dynamic pair      123
Sturm (set of recurrent Sturmian sequences)      104
Sublimb      20
Sublimb of denominator q      20
Substantially equal      26
Suspension      189
Tent map      185
Topological dynamical system      4
Touching chords      32
Translation principle      22
Translation-equivalent      22
tuning      20
Tuning in ${\mathbb T}/\sim$       99
Visibility tree      22
Visible chord in ${\mathcal B}_{*}$       80
Visible chord in ${\mathcal B}_{*},$ immediately      80
Visible hyperbolic component      22
W * d (tuning of parameter d associated to a hyperbolic component W)      20
W(n) (n-th symbol of a word w)      25
Wake      17
Word, $\alpha$ -regular      31

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