Interesting examples in \(\mathbb{C}^2\) of maps tangent to the identity without domains of attraction

DOI10.4171/JFG/84zbMath1445.37035arXiv1604.01366OpenAlexW2988550738MaRDI QIDQ2176596

Sara Lapan

Publication date: 5 May 2020

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.01366

zbMATH Keywords

fixed pointdomain of attractionholomorphic dynamicscharacteristic directionmaps tangent to the identityfixed curve

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) Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps (37F44) Higher-dimensional holomorphic and meromorphic dynamics (37F80)

Cites Work

• Poincaré-Bendixson theorems for meromorphic connections and holomorphic homogeneous vector fields
• Attracting domains for semi-attractive transformations of \(\mathbb{C}^ p\)
• Analytic transformations of \((\mathbb{C}^p,0)\) tangent to the identity
• ATTRACTING DOMAINS OF MAPS TANGENT TO THE IDENTITY WHOSE ONLY CHARACTERISTIC DIRECTION IS NON-DEGENERATE
• On \'Ecalle-Hakim's theorems in holomorphic dynamics
• Discrete holomorphic local dynamical systems

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