Non-recurrence of \(\exp(z)/z\)

DOI10.1007/s10114-012-1451-yzbMath1291.37074OpenAlexW2106285615MaRDI QIDQ1944847

Guoping Zhan

Publication date: 28 March 2013

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-012-1451-y

zbMATH Keywords

Julia set\(\omega\)-limit setnon-recurrencenesting condition

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)

Related Items (4)

Julia set of \(\lambda \exp(z)/z\) with real parameters \(\lambda\) ⋮ Most of the maps near have empty Fatou sets ⋮ Hausdorff dimension of a dynamically defined set of exp(z)/z ⋮ The M-set of λ exp(z)/z has infinite area

Cites Work

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• Weakly compact imbeddings of symmetric spaces
• Bifurcations in the space of exponential maps
• The exponential map is not recurrent
• Iterates of meromorphic functions. IV: Critically finite functions
• Most of the Maps near the Exponential are Hyperbolic
• Structural Instability of exp(z)
• 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)
• Area of Fatou sets of trigonometric functions

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