The Fatou set for critically finite maps

DOI10.1090/S0002-9939-08-09358-1zbMath1151.37045arXivmath/0608477OpenAlexW2024558509MaRDI QIDQ3533879

Feng Rong

Publication date: 24 October 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608477

zbMATH Keywords

basins of attractionpolymomial mapssuperattracting periodic points

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (9)

Post-critically finite maps on ℙⁿ for 𝕟≥2 are sparse ⋮ Algebraic webs invariant under endomorphisms ⋮ Periodic points of post-critically algebraic holomorphic endomorphisms ⋮ Structure of Julia sets for post-critically finite endomorphisms on \(\mathbb{P}^2\) ⋮ Periodic points of weakly post-critically finite all the way down maps ⋮ Attracting cycles in \(p\)-adic dynamics and height bounds for postcritically finite maps ⋮ Lattès maps on \(\mathbb P^2\) ⋮ Dynamics of post-critically finite maps in higher dimension ⋮ Fixed points of Koch maps

Cites Work

• Complex Hénon mappings in \({\mathbb{C}}^ 2\) and Fatou-Bieberbach domains
• Critical orbits of holomorphic maps on projective spaces
• Some properties of 2-critically finite holomorphic maps of ${\bf P}^2$
• Dynamics in One Complex Variable. (AM-160)
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