In mathematics, the Fatou conjecture, named after Pierre Fatou, states that a quadratic family of maps from the complex plane to itself is hyperbolic for...

0834.01. Fatou conjecture Fatou's theorem Fatou set Fatou–Lebesgue theorem (same as Fatou's lemma) Classification of Fatou components Fatou–Bieberbach...

problems in mathematics The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple...

attractor. Eremenko's conjecture: every component of the escaping set of an entire transcendental function is unbounded. Fatou conjecture that a quadratic...

convergence to zero coefficients (1912). This example disproved the Pierre Fatou conjecture and was unexpected to most mathematicians at that time. At approximately...

conjecture can be traced back to Fatou in the 1920s, and later Smale posed it in the 1960s. The proof of Real Fatou conjecture is one of the most important...

dynamics, a field first investigated by the French mathematicians Pierre Fatou and Gaston Julia at the beginning of the 20th century. The fractal was first...

by a p-adic field such as Qp or Cp and studies chaotic behavior and the Fatou and Julia sets. The following table describes a rough correspondence between...

Journal. With Jacek Graczyk he provided a rigorous proof of the real Fatou conjecture. Świątek was an invited speaker at International Congress of Mathematicians...

variables, where he obtained results similar to Fatou's. In 1916 he formulated the Bieberbach conjecture, stating a necessary condition for a holomorphic...

condition), thus solving an open problem since Fatou conjectured his theorem on the Classification of Fatou components. Later Alexander D. Brjuno improved...

long-standing open problems. In his Master's thesis, he proved a conjecture of Fatou from 1920 by showing that a rational function of degree d {\displaystyle...

denotes the Riemann sphere. More precisely, for every component U in the Fatou set of f, the sequence U , f ( U ) , f ( f ( U ) ) , … , f n ( U ) , … {\displaystyle...

discontinuities – Mathematical analysis of discontinuous points Classification of Fatou components Ratner classification theorem Classification of electromagnetic...

Ackermann function Horseshoe map Hénon map Arnold's cat map Population dynamics Fatou set Julia set Mandelbrot set Recurrence relation Matrix difference equation...

iteration of transcendental entire functions was first studied by Pierre Fatou in 1926 The escaping set occurs implicitly in his study of the explicit...

482–490. Retrieved July 19, 2019. Wolff, T. H. (1986). "Generalizations of Fatou's theorem". Proceedings of the International Congress of Mathematicians,...

(1985). "Quasiconformal homeomorphisms and dynamics I. Solution of the Fatou-Julia problem on wandering domains". Annals of Mathematics. 122 (2): 401–418...

out of proofs). See also list of axioms, list of theorems and list of conjectures. Abhyankar's lemma Aubin–Lions lemma Bergman's diamond lemma Fitting...

precolonial capital of Saloum). His maternal nephew, Maad a Sinig Niokhobaye Fatou Diène Diouf, from the Royal House of Semou Njekeh Joof was crowned King...

include: List of algebras List of algorithms List of axioms List of conjectures List of data structures List of derivatives and integrals in alternative...

where Lieb solved several important conjectures about operator inequalities, including the Wigner-Yanase-Dyson conjecture. In the years 1997–99, Lieb provided...

the Julia sets of rational maps R(z). Sullivan (1985) proved that if the Fatou set of R has two components and the action of R on the Julia set is "hyperbolic"...

invents algorithm for symbolic integration. Mandelbrot, from studies of the Fatou, Julia and Mandelbrot sets, coined and popularized the term 'fractal' to...

for meromorphic functions, Sci. China Ser. A, 48(2005), 262-267. p-Adic Fatou-Bieberbach mappings, Inter. J. Math, 16 (2005), No.3. Unique range sets...

biographer of Anna Kingsley, has based his account of her early life on conjecture based on his research into the history of the area. She was born Anta...

(2nd ed.), Springer (see Exercise (2.17) in Section V.2, page 187). See Fatou's theorem. Durrett, Richard (1984), Brownian motion and martingales in analysis...

Mandelbrot coins the term "fractal" to describe the self-similarity found in the Fatou, Julia and Mandelbrot sets. Fractals become the first mathematical visualization...

continuous if and only if { f } {\displaystyle \{f\}} is equicontinuous. Fatou Fatou's lemma Fock Fock space Fourier 1.  The Fourier transform of a function...