The real Fatou conjecture

The real Fatou conjecture /

The real Fatou conjecture /

In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it c...

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Bibliographic Details
Main Authors: Graczyk, Jacek, Świa̧tek, Grzegorz, 1964- (Author)
Format: Electronic eBook
Language:English
Published: Princeton, N.J. : Princeton University Press, 1998.
Series:Annals of mathematics studies ; no. 144.
Subjects:
Geodesics (Mathematics)
Mappings (Mathematics)
Polynomials.
Mathematik.
MATHEMATICS > Geometry > General.
MATHEMATICS > Complex Analysis.
Polynomials
Absolute value.
Affine transformation.
Algebraic function.
Analytic continuation.
Analytic function.
Arithmetic.
Automorphism.
Big O notation.
Bounded set (topological vector space)
C0.
Calculation.
Canonical map.
Change of variables.
Chebyshev polynomials.
Combinatorics.
Commutative property.
Complex number.
Complex plane.
Complex quadratic polynomial.
Conformal map.
Conjecture.
Conjugacy class.
Conjugate points.
Connected component (graph theory)
Connected space.
Continuous function.
Corollary.
Covering space.
Critical point (mathematics)
Dense set.
Derivative.
Diffeomorphism.
Dimension.
Disjoint sets.
Disjoint union.
Disk (mathematics)
Equicontinuity.
Estimation.
Existential quantification.
Fibonacci.
Functional equation.
Fundamental domain.
Generalization.
Great-circle distance.
Hausdorff distance.
Holomorphic function.
Homeomorphism.
Homotopy.
Hyperbolic function.
Imaginary number.
Implicit function theorem.
Injective function.
Integer.
Intermediate value theorem.
Interval (mathematics)
Inverse function.
Irreducible polynomial.
Iteration.
Jordan curve theorem.
Julia set.
Limit of a sequence.
Linear map.
Local diffeomorphism.
Mathematical induction.
Mathematical proof.
Maxima and minima.
Meromorphic function.
Moduli (physics)
Monomial.
Monotonic function.
Natural number.
Neighbourhood (mathematics)
Open set.
Parameter.
Periodic function.
Periodic point.
Phase space.
Point at infinity.
Polynomial.
Projection (mathematics)
Quadratic function.
Quadratic.
Quasiconformal mapping.
Renormalization.
Riemann sphere.
Riemann surface.
Schwarzian derivative.
Scientific notation.
Subsequence.
Theorem.
Theory.
Topological conjugacy.
Topological entropy.
Topology.
Union (set theory)
Unit circle.
Unit disk.
Upper and lower bounds.
Upper half-plane.
Z0.
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