A Family of Cubic Rational Maps and Matings of Cubic Polynomials

DOI10.1080/10586458.2000.10504634zbMath0969.37020OpenAlexW2023760090MaRDI QIDQ4506288

Mitsuhiro Shishikura, Lei Tan

Publication date: 12 March 2001

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

Full work available at URL: https://projecteuclid.org/euclid.em/1046889589

zbMATH Keywords

Levy cyclesmating of polynomialsThurston obstructions

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (22)

Matings of cubic polynomials with a fixed critical point. Part II: α-symmetry of limbs ⋮ Renormalizations and wandering Jordan curves of rational maps ⋮ From rubber bands to rational maps: a research report ⋮ Mating non-renormalizable quadratic polynomials ⋮ Combination Theorems in Groups, Geometry and Dynamics ⋮ The Pullback Map on Teichmüller Space Induced from a Thurston Map ⋮ Pasting Together Julia Sets: A Worked Out Example of Mating ⋮ Algorithmic aspects of branched coverings IV/V. Expanding maps ⋮ Combining rational maps and Kleinian groups via orbit equivalence ⋮ A characterization of hyperbolic rational maps ⋮ Jordan mating is always possible for polynomials ⋮ A classification of bicritical rational maps with a pair of period two superattracting cycles ⋮ Tan Lei and Shishikura's example of non-mateable degree 3 polynomials without a Lévy cycle ⋮ Questions about polynomial matings ⋮ Algorithmic aspects of branched coverings ⋮ A decomposition theorem for Herman maps ⋮ An algebraic formulation of Thurston’s combinatorial equivalence ⋮ Newton maps as matings of cubic polynomials ⋮ A continuity result on quadratic matings with respect to parameters of odd denominator rationals ⋮ Thurston equivalence for rational maps with clusters ⋮ Circle packings, kissing reflection groups and critically fixed anti-rational maps ⋮ Mating Siegel quadratic polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• A partial description of parameter space of rational maps of degree two. I
• Complex dynamics
• A proof of Thurston's topological characterization of rational functions
• Combining rational maps and controlling obstructions

This page was built for publication: A Family of Cubic Rational Maps and Matings of Cubic Polynomials