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McMullen C., Kalpazidou S.L. — Complex dynamics and renormalization
McMullen C., Kalpazidou S.L. — Complex dynamics and renormalization

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Название: Complex dynamics and renormalization

Авторы: McMullen C., Kalpazidou S.L.


This work presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics.

Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an "infinitely renormalizable" quadratic polynomial "f(z) = z2 + c," As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial "f," This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set.

The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 214

Добавлена в каталог: 07.12.2009

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Предметный указатель
$\alpha$ fixed point      88
$\alpha$-lamination      130
$\beta$ fixed point      88
$\gamma_{n}(i)$      135
$\mathcal{SR}(f)$      111
$\mathcal{SR}(f)*$      135
Attracting      36
C(f)      67
Caratheodory topology      66
Collar      22
Critically finite      38
Crossed renormalization      111
Curve system      190
Cusp      24
CYCLE      36
Disk      66
Ergodic      42
Essential      11
Euler characteristic $\mathcal{X(O)}$      180
External ray      84
Fatou set      36
Feigenbaum polynomial      114
Filled Julia set      38
Full continuum      83
Hyperbolic metric      11
Hyperbolic rational map      45
Indifferent      36
Infinitely renormalizable      121
J(f)      36
Julia set      36
K(f)      38
K(f), polynomial-like      71
Koebe principle      15
Lamination      92
Lebesgue density      20
Line field      47
Local connectivity      128
Mandelbrot set      59
mod(A)      10
mod(E,V)      13
Modulus of an annulus      10
Montel's theorem      17
Multiplicity      113
Normal family      17
Orbifold      178
P(F)      38
Parabolic      36
Periodic point      36
Polynomial-like map      71
Postcritical set      38
Preperiodic      36
Proper map      67
Puzzle pieces      123
Quadratic-like map      97
Quasiconformal      18
Quotient map      188
Ramification      113
Rational lamination      92
Renormalization      98
Renormalization period      125
Repelling      36
Robust      138
Simple renormalization      111
Superattracting      36
Tableau      125
Torus endomorphism      48
tuning      118
Unbranched renormalization      143
Univalent line field      78
Univalent map      15
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