Capture Zones of the Family of Functions λzmexp(z)

DOI10.1142/S0218127403008120zbMath1052.37038arXivmath/0207103OpenAlexW1592236894MaRDI QIDQ3046557

Antonio Garijo, Núria Fagella

Publication date: 12 August 2004

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0207103

zbMATH Keywords

invariant setbasin of attractioncritical pointexponential mapcapture zonesuperattracting fixed point

Mathematics Subject Classification ID

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) 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 (9)

Iteration of certain exponential-like meromorphic functions ⋮ Joining polynomial and exponential combinatorics for some entire maps ⋮ Convergence of rays with rational argument in hyperbolic components—an illustration in transcendental dynamics ⋮ Classifying simply connected wandering domains ⋮ Dynamical convergence of polynomials to products of power maps and the exponential ⋮ The parameter planes of \(\lambda z^m \exp(z)\) for \(m \geq 2\) ⋮ Connectedness of the Arnold tongues for double standard maps ⋮ Relating singularly perturbed rational maps to families of entire maps ⋮ On the formulas of meromorphic functions with periodic Herman rings

Cites Work

• Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains
• Uniformization of attracting basins for exponential maps
• Siegel discs, Herman rings and the Arnold family
• Some connectedness properties of julia sets
• LIMITING DYNAMICS FOR THE COMPLEX STANDARD FAMILY
• Invariant domains and singularities

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