The iteration of cubic polynomials. II: Patterns and parapatterns
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Publication:1336308
DOI10.1007/BF02392761zbMath0812.30008OpenAlexW2011962615MaRDI QIDQ1336308
John H. Hubbard, Bodil Branner
Publication date: 16 May 1995
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02392761
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)
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Cites Work
- Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains
- The iteration of cubic polynomials. I: The global topology of parameter space
- Hénon mappings in the complex domain. I: The global topology of dynamical space
- Invariant sets under iteration of rational functions
- On the dynamics of rational maps
- On the dynamics of polynomial-like mappings
- A proof of the generalized Schoenflies theorem
- Unnamed Item
- Unnamed Item
- Unnamed Item
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