Dynamical convergence of polynomials to products of power maps and the exponential

zbMath1521.37042MaRDI QIDQ6044924

Devin Becker, Lorelei Koss, Joanna Furno

Publication date: 25 May 2023

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://nyjm.albany.edu/j/2023/29-19.html

zbMATH Keywords

Julia setsentire functionscomplex dynamicsrational maps

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets (37F46)

Cites Work

• Dynamical properties of some classes of entire functions
• The parameter planes of \(\lambda z^m \exp(z)\) for \(m \geq 2\)
• Hausdorff convergence of Julia sets
• Rational families converging to a family of exponential maps
• Capture Zones of the Family of Functions λz^mexp(z)
• Dynamical convergence of a certain polynomial family to f_a(z) = z + e^z + a
• Hyperbolic components of polynomials with a fixed critical point of maximal order
• HAIRS FOR THE COMPLEX EXPONENTIAL FAMILY
• The boundaries of certain normality domains for rational maps
• On the dynamics of polynomial-like mappings
• Local connectedness of the Julia set of the family $z^m(z^n-b)$
• CONVERGENCE OF JULIA SETS IN THE APPROXIMATION OF λe^z BY λ[1+(z/d)^d]
• Kernel convergence of hyperbolic components
• Hausdorff Convergence and the Limit Shape of the Unicorns
• LIMITING DYNAMICS FOR THE COMPLEX STANDARD FAMILY
• A note on non-converging Julia sets
• The connectedness locus of the family of polynomialsP_c(z) = zⁿ–cz
• A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j
• Geometric limits of Julia  sets and connectedness locus of the family of polynomials P_c(z) = zⁿ + cz^k
• Homeomorphisms between limbs of the Mandelbrot set
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