The M-set of λ exp(z)/z has infinite area
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Publication:5256673
DOI10.1215/00277630-2888085zbMath1362.37094OpenAlexW1768009849MaRDI QIDQ5256673
Publication date: 19 June 2015
Published in: Nagoya Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://projecteuclid.org/euclid.nmj/1430939249
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) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50)
Related Items (4)
CONSTRUCTION AND ANALYSIS OF A SPECIAL ONE-DIMENSIONAL CONTINUOUS FUNCTION ⋮ Julia set of \(\lambda \exp(z)/z\) with real parameters \(\lambda\) ⋮ Most of the maps near have empty Fatou sets ⋮ Hausdorff measure of the escaping parameter without endpoints is zero for exponential family
Cites Work
- Bifurcations in the space of exponential maps
- Uniformization of attracting basins for exponential maps
- Iterates of meromorphic functions. IV: Critically finite functions
- Complex dynamics
- Non-recurrence of \(\exp(z)/z\)
- Julia sets and bifurcation diagrams for exponential maps
- Most of the Maps near the Exponential are Hyperbolic
- The escaping set of the exponential
- Area and Hausdorff Dimension of Julia Sets of Entire Functions
- On iterates of ez
- Iteration of meromorphic functions
- Hausdorff dimension of theM-set of λ exp(z)
- Hyperbolic components of the complex exponential family
- Topological dynamics of exponential maps on their escaping sets
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