On Rational Maps with Two Critical Points

DOI10.1080/10586458.2000.10504657zbMath0972.30013arXivmath/9709226OpenAlexW2027691611MaRDI QIDQ2706534

John W. Milnor

Publication date: 19 March 2001

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9709226

zbMATH Keywords

fixed pointJulia setsmultiplierrational mapsquasiconformal surgerymarked point

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (34)

Connectivity of Julia sets for Weierstrass elliptic functions on square lattices ⋮ Julia sets of cubic rational maps with escaping critical points ⋮ Families of ergodic and exact one-dimensional maps ⋮ Non-landing parameter rays of the multicorns ⋮ Cubic rational maps with escaping critical points. I: Julia set dichotomy in the case of an attracting fixed point ⋮ Julia sets on ℝℙ² and dianalytic dynamics ⋮ Dynamics of regularly ramified rational maps. I: Julia sets of maps in one-parameter families ⋮ Lee-Yang zeros of the antiferromagnetic Ising model ⋮ A family of rational maps with buried Julia components ⋮ Bounded hyperbolic components of bicritical rational maps ⋮ Cantor and connected Julia sets of the parameterized Dixon elliptic functions ⋮ A compactification of the moduli space of self-maps of $\mathbb {CP}^1$ via stable maps ⋮ Rational maps without Herman rings ⋮ Dynamics of Schwarz Reflections: The Mating Phenomena ⋮ Blowup points and baby Mandelbrot sets for a family of singularly perturbed rational maps ⋮ Lebesgue measure theoretic dynamics of rational maps ⋮ Characterizing indecomposable plane continua from their complements ⋮ No Herman rings for regularly ramified rational maps ⋮ Parameter space for families of parabolic-like mappings ⋮ Rational families converging to a family of exponential maps ⋮ DYNAMICS AND BIFURCATIONS OF A FAMILY OF RATIONAL MAPS WITH PARABOLIC FIXED POINTS ⋮ Invisible tricorns in real slices of rational maps ⋮ On the dynamics of a family of generated renormalization transformations ⋮ On the non-monotonicity of entropy for a class of real quadratic rational maps ⋮ Bifurcations in the space of exponential maps ⋮ Quadratic rational maps lacking period 2 orbits ⋮ Thurston equivalence for rational maps with clusters ⋮ Connectivity properties of Julia sets of Weierstrass elliptic functions ⋮ On the formulas of meromorphic functions with periodic Herman rings ⋮ On real and pseudo-real rational maps ^* ⋮ Discontinuity of Straightening in Anti-holomorphic Dynamics: I ⋮ Perturbing Misiurewicz parameters in the exponential family ⋮ Monotonicity of entropy for real quadratic rational maps ⋮ Unnamed Item

Cites Work

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• The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift
• Components of degree two hyperbolic rational maps
• Complex dynamics
• Symmetries of fractals revisited
• The space of rational maps on \(\mathbf P^1\)
• On the dynamics of polynomial-like mappings
• Positive measure sets of ergodic rational maps
• On the quasiconformal surgery of rational functions
• Matings of quadratic polynomials
• The rational maps $z\mapsto 1+1/\omega z^d$ have no Herman rings
• Iteration of meromorphic functions
• Geometry and Dynamics of Quadratic Rational Maps
• e^z: DYNAMICS AND BIFURCATIONS

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