Dynamics in one complex variable

By John W. Milnor. 2000

1,728 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/99d67821a41a6ad47d8d71a287d7a83099544072

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computational Theory and Mathematics

Citations in the corpus

Sierpinski-curve Julia sets and singular perturbations of complex polynomials (2005, background): “Hence, U is a Cantor set and, just as in the case of quadratic polynomials with critical orbits that escape to ∞ (see [1, 6]), F | U is conjugate to the one-sided shift on two symbols.”
Espace hyperbolique p-adique et dynamique des fonctions rationnelles (2003, background): “Dans cette section on considère l’ensemble exceptionnel de l’action sur Hp induite par une fonction rationnelle ; comme dans le cas complexe pour les fonctions rationnelles, voir par exemple [Mi].”
Classification of invariant Fatou components for dissipative Hénon maps (2014, background): “Topological proof The following argument was proposed to us by Gabrielov and Milnor.”
Hyperbolicity of renormalization of critical circle maps (2003, background): “i( f , z0) = 1 2πi ∮ dz z − f (z) where the integrating is done over a small contour enclosing z0 (see [Mil]).”
Siegel disks with smooth boundaries (2004, background): “It is known since Fatou that this boundary is contained in the closure of the forward orbit of the critical point !fi = ie2i…fi=2 (for example, see [Mi] Theorem 11.17 or [ Mi ] Corollary 14.4).”
Expanding Thurston Maps (2010, methodology): “1 is well known (see, for example, [Mi06a]).”
Distributions in algebraic dynamics (2005, methodology): “We refer to Katok and Hasselblatt’s book [32] for dynamics on manifolds, Milnor’s book [41] for P1, Sibony’s article [54] for PN , and Dinh-Sibony [21] for general complex variety respectively.”
Rigidity of escaping dynamics for transcendental entire functions (2006, background): “Proof. Recall that the existence of an invariant line field is equivalent to the existence of a non-zero F-invariant Beltrami form whose support is contained in I(F) [ McM2 , Section 3.5].”
Return time statistics via inducing (2000, background): “Using the arguments in [27], one can show that the diameters of the elements Y ∈ Pi tend to 0 as i→ ∞, unless Y eventually intersects a Siegel disk.”