Faria - Mathematical Tools for One Dimensional Dynamics (Cambridge, 2008).pdf

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CAMBRIDGE STUDIES IN ADVANCED
MATHEMATICS 115
EDITORIAL BOARD
b. bollobas, w. fulton, a. katok, f. kirwan,
p. sarnak, b. simon, b. totaro
Mathematical Tools for One-Dimensional Dynamics
Originating with the pioneering works of P. Fatou and G. Julia, the subject
of complex dynamics has seen great advances in recent years. Complex
dynamical systems often exhibit rich, chaotic behavior, which yields
attractive computer generated pictures, for example the Mandelbrot and
Julia sets, which have done much to renew interest in the subject.
In this self-contained book, the major mathematical tools necessary for
the study of complex dynamics at an advanced level are discussed. Complete
proofs of some of these tools are presented; some, such as the Bers–Royden
theorem on holomorphic motions, appear for the first time in book format.
Riemann surfaces and Teichmuller theory are considered in an appendix.
Detailing the latest research, the book will appeal to graduate students and
researchers working in dynamical systems and related fields. Carefully
chosen exercises aid understanding and provide a glimpse of further
developments in real and complex one-dimensional dynamics.
CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS
Editorial Board:
B. Bollobas, W. Fulton, A. Katok, F. Kirwan, P. Sarnak, B. Simon, B. Totaro
All the titles listed below can be obtained from good booksellers or from
Cambridge University Press. For a complete series listing visit:
http://www.cambridge.org/series/sSeries.asp?code=CSAM
Already published
68 K. Sato Levy Processes and Infinitely Divisible Distributions
69 H. Hida Modular Forms and Galois Cohomology
70 R. Iorio & V. Iorio Fourier Analysis and Partial Differential Equations
71 R. Blei Analysis in Integer and Fractional Dimensions
72 F. Borceaux & G. Janelidze Galois Theories
73 B. Bollobas Random Graphs
74 R. M. Dudley Real Analysis and Probability
75 T. Sheil-Small Complex Polynomials
76 C. Voisin Hodge Theory and Complex Algebraic Geometry, I
77 C. Voisin Hodge Theory and Complex Algebraic Geometry, II
78 V. Paulsen Completely Bounded Maps and Operator Algebras
79 F. Gesztesy & H. Holden Soliton Equations and Their Algebro-Geometric
Solutions, I
81 S. Mukai An Introduction to Invariants and Moduli
82 G. Tourlakis Lectures in Logic and Set Theory, I
83 G. Tourlakis Lectures in Logic and Set Theory, II
84 R. A. Bailey Association Schemes
85 J. Carlson, S. Muller-Stach & C. Peters Period Mappings and Period Domains
86 J. J. Duistermaat & J. A. C. Kolk Multidimensional Real Analysis I
87 J. J. Duistermaat & J. A. C. Kolk Multidimensional Real Analysis II
89 M. Golumbic & A. Trenk Tolerance Graphs
90 L. Harper Global Methods for Combinatorial Isoperimetric Problems
91 I. Moerdijk & J. Mrcun Introduction to Foliations and Lie Groupoids
92 J. Kollar, K. E. Smith & A. Corti Rational and Nearly Rational Varieties
93 D. Applebaum Levy Processes and Stochastic Calculus
94 B. Conrad Modular Forms and the Ramanujan Conjecture
95 M. Schechter An Introduction to Nonlinear Analysis
96 R. Carter Lie Algebras of Finite and A ne Type
97 H. L. Montgomery, R. C. Vaughan & M. Schechter Multiplicative Number
Theory, I
98 I. Chavel Riemannian Geometry
99 D. Goldfeld Automorphic Forms and L-Functions for the Group GL(n,R)
100 M. Marcus & J. Rosen Markov Processes. Gaussian Processes, and Local Times
101 P. Gille & T. Szamuely Central Simple Algebras and Galois Cohomology
102 J. Bertoin Random Fragmentation and Coagulation Processes
103 E. Frenkel Langlands Correspondence for Loop Groups
104 A. Ambrosetti & A. Malchiodi Nonlinear Analysis and Semilinear Elliptic
Problems
105T.Tao&V.H.Vu Additive Combinatorics
106 E. B. Davies Linear Operators and their Spectra
107 K. Kodaira Complex Analysis
108 T. Ceccherini-Silberstein, F. Scarabotti & F. Tolli Harmonic Analysis on Finite
Groups
109 H. Geiges An Introduction to Contact Topology
110 J. Faraut Analysis on Lie Groups
111 E. Park Complex Topological K-Theory
112 D. W. Stroock Partial Differential Equations for Probabilists
113 A. Kirillov An Introduction to Lie Groups and Lie Algebras
114 F. Gesztesy, H. Holden, J. Michor & G. Teschl Soliton Equations and their
Algebro-Geometric Solutions, II
115 Edson de Faria & Welington de Melo Mathematical Tools for One-Dimensional
Dynamics
Mathematical Tools for
One-Dimensional Dynamics
EDSON DE FARIA
IME-USP, Sao Paulo
WELINGTON DE MELO
IMPA, Rio de Janeiro
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