Dynamics in One Complex Variable
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A01=John Milnor
Absolute value
Algebraic equation
Author_John Milnor
Automorphism
Beltrami equation
Boundary (topology)
Branched covering
Category=PBKD
Coefficient
Compact Riemann surface
Compact space
Complex analysis
Complex number
Complex plane
Computation
Connected component (graph theory)
Connected space
Continued fraction
Continuous function
Corollary
Covering space
Cross-ratio
Derivative
Diagram (category theory)
Diameter
Diffeomorphism
Disjoint sets
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Euler characteristic
Existential quantification
Fundamental group
Holomorphic function
Homeomorphism
Hyperbolic geometry
Inequality (mathematics)
Integer
Iteration
Jordan curve theorem
Julia set
Limit point
Line segment
Linear map
Open set
Orbifold
Parameter
Parameter space
Periodic point
Point at infinity
Polynomial
Quadratic function
Rational function
Rational number
Real number
Riemann sphere
Riemann surface
Rotation number
Schwarz lemma
Scientific notation
Sequence
Simply connected space
Special case
Subgroup
Subsequence
Subset
Summation
Tangent space
Theorem
Topological space
Uniformization theorem
Unit circle
Unit disk
Upper half-plane
Product details
- ISBN 9780691124889
- Weight: 539g
- Dimensions: 178 x 254mm
- Publication Date: 22 Jan 2006
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattes map has been made more inclusive, and the ecalle-Voronin theory of parabolic points is described. The residu iteratif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.
John Milnor is Professor of Mathematics and Co-Director of the Institute for Mathematical Sciences at SUNY, Stony Brook. He is the author of "Topology from the Differential Viewpoint, Singular Points of Complex Hypersurfaces, Morse Theory, Introduction to Algebraic K-Theory, Characteristic Classes" (with James Stasheff), and "Lectures on the H-Cobordism Theorem" (Princeton).
