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Dynamics in One Complex Variable
John Milnor
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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 Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif 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.
Kundenbewertungen
Rational number, Euler characteristic, Parameter space, Diagram (category theory), Boundary (topology), Inequality (mathematics), Integer, Connected space, Upper half-plane, Computation, Rational function, Topological space, Diameter, Coefficient, Holomorphic function, Unit circle, Branched covering, Summation, Algebraic equation, Equation, Line segment, Absolute value, Disjoint sets, Iteration, Uniformization theorem, Existential quantification, Connected component (graph theory), Open set, Simply connected space, Corollary, Periodic point, Complex number, Subset, Complex analysis, Parameter, Scientific notation, Subsequence, Riemann sphere, Unit disk, Orbifold, Schwarz lemma, Tangent space, Continued fraction, Rotation number, Automorphism, Derivative, Polynomial, Complex plane, Diffeomorphism, Compact space, Homeomorphism, Sequence, Theorem, Hyperbolic geometry, Continuous function, Riemann surface, Limit point, Real number, Covering space, Cross-ratio, Special case, Fundamental group, Jordan curve theorem, Point at infinity, Julia set, Linear map, Quadratic function, Compact Riemann surface, Beltrami equation, Subgroup