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Dynamics in one complex variable [[electronic resource] /] / by John Milnor



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Autore: Milnor John W (John Willard), <1931-> Visualizza persona
Titolo: Dynamics in one complex variable [[electronic resource] /] / by John Milnor Visualizza cluster
Pubblicazione: Princeton, N.J., : Princeton University Press, 2006
Edizione: 3rd ed.
Descrizione fisica: 1 online resource (313 p.)
Disciplina: 515.93
515/.93
Soggetto topico: Functions of complex variables
Holomorphic mappings
Riemann surfaces
Soggetto non controllato: Absolute value
Addition
Algebraic equation
Attractor
Automorphism
Beltrami equation
Blaschke product
Boundary (topology)
Branched covering
Coefficient
Compact Riemann surface
Compact space
Complex analysis
Complex number
Complex plane
Computation
Connected component (graph theory)
Connected space
Constant function
Continued fraction
Continuous function
Coordinate system
Corollary
Covering space
Cross-ratio
Derivative
Diagram (category theory)
Diameter
Diffeomorphism
Differentiable manifold
Disjoint sets
Disjoint union
Disk (mathematics)
Division by zero
Equation
Euler characteristic
Existential quantification
Exponential map (Lie theory)
Fundamental group
Harmonic function
Holomorphic function
Homeomorphism
Hyperbolic geometry
Inequality (mathematics)
Integer
Inverse function
Irrational rotation
Iteration
Jordan curve theorem
Julia set
Lebesgue measure
Lecture
Limit point
Line segment
Linear map
Linearization
Mandelbrot set
Mathematical analysis
Maximum modulus principle
Metric space
Monotonic function
Montel's theorem
Normal family
Open set
Orbifold
Parameter space
Parameter
Periodic point
Point at infinity
Polynomial
Power series
Proper map
Quadratic function
Rational approximation
Rational function
Rational number
Real number
Riemann sphere
Riemann surface
Root of unity
Rotation number
Schwarz lemma
Scientific notation
Sequence
Simply connected space
Special case
Subgroup
Subsequence
Subset
Summation
Tangent space
Theorem
Topological space
Topology
Uniform convergence
Uniformization theorem
Unit circle
Unit disk
Upper half-plane
Winding number
Classificazione: SI 830
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references (p. 277-291) and index.
Nota di contenuto: Frontmatter -- Table Of Contents -- List of Figures -- Preface to the Third Edition -- Chronological Table -- Riemann Surfaces -- Iterated Holomorphic Maps -- Local Fixed Point Theory -- Periodic Points: Global Theory -- Structure of the Fatou Set -- Using the Fatou Set to Study the Julia Set -- Appendix A. Theorems from Classical Analysis -- Appendix B. Length-Area-Modulus Inequalities -- Appendix C. Rotations, Continued Fractions, and Rational Approximation -- Appendix D. Two or More Complex Variables -- Appendix E. Branched Coverings and Orbifolds -- Appendix F. No Wandering Fatou Components -- Appendix G. Parameter Spaces -- Appendix H. Computer Graphics and Effective Computation -- References -- Index
Sommario/riassunto: 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.
Titolo autorizzato: Dynamics in one complex variable  Visualizza cluster
ISBN: 1-283-00148-9
9786613001481
1-4008-3553-4
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910791879203321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: Annals of mathematics studies ; ; no. 160.