Julia set of \(\lambda \exp(z)/z\) with real parameters \(\lambda\)

DOI10.1007/s13226-017-0225-8zbMath1387.37042OpenAlexW2755934709WikidataQ121864815 ScholiaQ121864815MaRDI QIDQ1702457

Guoping Zhan

Publication date: 28 February 2018

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-017-0225-8

zbMATH Keywords

Julia setHausdorff dimensionmeromorphic functionFatou set

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)

Cites Work

• The exponential map is not recurrent
• Julia set of the function \(z\exp(z+\mu)\)
• Julia set of the function \(z\text{ exp}(z+\mu)\). II
• Non-recurrence of \(\exp(z)/z\)
• Hausdorff dimension of a dynamically defined set of exp(z)/z
• Most of the Maps near the Exponential are Hyperbolic
• Structural Instability of exp(z)
• Wandering domains for maps of the punctured plane
• Area and Hausdorff Dimension of Julia Sets of Entire Functions
• On iterates of e^z
• Iteration of meromorphic functions
• Hausdorff dimension of theM-set of λ exp(z)
• The M-set of λ exp(z)/z has infinite area
• Most of the maps near have empty Fatou sets
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