Hausdorff dimension of theM-set of λ exp(z)

DOI10.1007/BF02582032zbMath0817.30011MaRDI QIDQ4323165

Wei-Yuan Qiu

Publication date: 18 July 1995

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

zbMATH Keywords

iterationJulia setHausdorff dimension

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05)

Related Items (17)

The dimension paradox in parameter space of cosine family ⋮ Non-recurrence of \(\exp(z)/z\) ⋮ Speiser meets Misiurewicz ⋮ Julia set of \(\lambda \exp(z)/z\) with real parameters \(\lambda\) ⋮ Hausdorff Dimension of Sets of Escaping Points and Escaping Parameters for Elliptic Functions ⋮ Most of the maps near have empty Fatou sets ⋮ Escaping points and escaping parameters for singly periodic meromorphic maps: Hausdorff dimensions outlook ⋮ Hausdorff measure of the escaping parameter without endpoints is zero for exponential family ⋮ Most of the Maps near the Exponential are Hyperbolic ⋮ Indecomposable continua in exponential dynamics -- Hausdorff dimension ⋮ Classification of escaping exponential maps ⋮ Hausdorff dimension of a dynamically defined set of exp(z)/z ⋮ Parameter rays in the space of exponential maps ⋮ Perturbing Misiurewicz parameters in the exponential family ⋮ The M-set of λ exp(z)/z has infinite area ⋮ Geometry and ergodic theory of non-hyperbolic exponential maps ⋮ The Hausdorff dimension of directional edge escaping points set

Cites Work

• Iteration of exponential functions
• Julia sets and bifurcation diagrams for exponential maps
• Area and Hausdorff Dimension of Julia Sets of Entire Functions
• A finiteness theorem for a dynamical class of entire functions
• On iterates of e^z
• Unnamed Item
• Unnamed Item

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