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Beardon A.F. — Iteration of rational functions
Beardon A.F. — Iteration of rational functions



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Название: Iteration of rational functions

Автор: Beardon A.F.

Аннотация:

This book makes available a comprehensive, detailed, and organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The material covered extends from the original memoirs of Fatou and Julia to the recent and important results and methods of Sullivan and Shishikura. Many of the details of the proofs have not occurred in print before. The theory of of dynamical systems and chaos has recently undergone a rapid growth in popularity, in part due to the spectacular computer graphics of Julia sets, fractals, and the Mandelbrot set. This text focuses on the specialized area of complex analytic dynamics, a subject that dates back to 1916 and is currently a very active area in mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 280

Добавлена в каталог: 04.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Analytic function      31
Arzela — Ascoli theorem      56
Automorphic functions      12
Automorphism (of a domain)      162
Backward invariant set      51
Backward orbit      66
Basin (of a cycle)      104
Beltrami equation (coefficient)      180
Branches (of inverse map)      43
Buried component (of J)      266
Cantor set      21 227 250 266
Cayley      23
Centroid (of a polynomial)      205
Chain Rule (for valency)      37
Chordal metric      28
Complementary components (of a curve)      35
Completely invariant set      51 53
Complex dilatation      180
Complex projective space      47
Conformal structure      181
Conjugate (conjugacy)      11 36 105 150
Connectivity (of a domain)      80
Cover group      157
Critical point      43
Critical value      3
CYCLE      100
D-fold map      31
Deficiency      86
Degree (of rational map)      30
Dendrite      258
Directed set      90
Displacement function      184
Elliptic function      74 77
Equicontinuity      49 50
Euler characteristic      83 84
Eventually periodic domain      176
Exceptional point      65
Expanding maps      225
Extended complex plane      27
Exterior (of a curve)      35
Fatou (set)      3 50
Fixed point (attracting, super-attracting, Repelling, indifferent)      2 38 99
Fixed point at infinity      39
Fold (e.g., d-fold map)      31
Forward invariant set      51 161
Forward orbit      76 192
Genus      85
Green's function      206 240
Hausdorff dimension (measure)      247 251
Herman ring      160
Holomorphic function      30
Hyperbolic geometry (metric)      59 60 157
Infinite products      155
Interior components (of a curve)      35
Invariant set      51
Isolated points      68
Isometry      28
Iteration      1
Jordan curve      233
Julia (set)      3 50
Lattes      73
Limit function      162
Linearizable      109 132
Linearly ordered set      81
Lipschitz condition      32
Locally uniform convergence      55
Logistic map      17
Mandelbrot set      17 238
Meromorphic function      30
Minimality (of J)      68
Mobius transformation      3
Multiplier      40 100
Net      90
Newton — Raphson approximation      23
Normal family      55
Normality (set of)      50
normalizer      159
Orbit (great orbit)      53
Parabolic component (of F)      160
Perfect set      68
Period doubling      17
Periodic points      7 70 100
Petal Theorem      116 131
Petals      114
Pre-periodic point      75 100
Quasiconformal map      180
Quasiregular function      210
Rational map      30
Regular subdomain      90
Riemann — Hurwitz relation      43 52 86 92
Schwarz lemma      59 64 158
Self-similarity      250
Semi-conjugate      11
Set of normality      50
Shift map      230 232
Siegel disc      134 160
Simply connected domain      80
Spherical metric      29
Stable set      50 104
Stereographic projection      27
Symmetry group (of J)      204
Tchebychev polynomials      9
Triangulation      83
Univalent function      38
Universal covering surface      157
Valency      37
Vitali's theorem      56
Wandering domain      176
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