A01=Curtis T. McMullen
Analytic function
Author_Curtis T. McMullen
Automorphism
Category=PBK
Category=PBV
Coefficient
Combinatorics
Complex manifold
Complex plane
Complex torus
Conformal geometry
Conjecture
Covering space
Cyclic group
Degeneracy (mathematics)
Diagram (category theory)
Differential geometry of surfaces
Dihedral group
Dimension (vector space)
Disk (mathematics)
Endomorphism
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equivalence class
Ergodic theory
Euler characteristic
Geometric function theory
Hausdorff dimension
Holomorphic function
Homology (mathematics)
Hyperbolic geometry
Injective function
Julia set
Kleinian group
Limit point
Linear map
Mandelbrot set
Manifold
Markov partition
Mathematical induction
Maxima and minima
Measure (mathematics)
Mobius transformation
Moduli (physics)
Monic polynomial
Montel's theorem
Open set
Orbifold
Periodic point
Permutation
Point at infinity
Pole (complex analysis)
Polynomial
Quadratic differential
Quadratic function
Quasi-isometry
Quasiconformal mapping
Quotient space (topology)
Removable singularity
Renormalization
Riemann mapping theorem
Riemann sphere
Riemann surface
Rigidity theory (physics)
Scalar (physics)
Schwarz lemma
Scientific notation
Special case
Subsequence
Symbolic dynamics
Tangent space
Theorem
Uniformization
Uniformization theorem
Unit disk
Product details
- ISBN 9780691029818
- Weight: 312g
- Dimensions: 197 x 254mm
- Publication Date: 19 Dec 1994
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.
Curtis T. McMullen is Professor of Mathematics at the University of California, Berkeley.
