Basins of attraction in quadratic dynamical systems with a Jordan fixed point

DOI10.1016/S0362-546X(01)00830-6zbMath1035.37032OpenAlexW2079428254MaRDI QIDQ697534

Marco Abate

Publication date: 17 September 2002

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(01)00830-6

zbMATH Keywords

basin of attractionparabolic fixed point

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50)

Related Items (3)

Fatou Flowers and Parabolic Curves ⋮ A Brief Survey on Local Holomorphic Dynamics in Higher Dimensions ⋮ Local dynamics of holomorphic maps in \(\mathbf C^{2}\) with a Jordan fixed point

Cites Work

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• Local structure of analytic transformations of two complex variables. I
• Attracting basins for automorphisms of \(\mathbb{C}^2\)
• Local structure of analytic transformations of two complex variables. II
• Complex dynamics
• The residual index and the dynamics of holomorphic maps tangent to the identity
• Attracting domains for semi-attractive transformations of \(\mathbb{C}^ p\)
• Analytic transformations of \((\mathbb{C}^p,0)\) tangent to the identity
• Stable curves asymptotic to a degenerate fixed point
• Diagonalization of nondiagonalizable discrete holomorphic dynamical systems
• Parabolic manifolds for semi-attractive holomorphic germs

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