Parameter rays in the space of exponential maps

DOI10.1017/S0143385708000394zbMath1160.37364MaRDI QIDQ3625423

Markus Förster, Dierk Schleicher

Publication date: 5 May 2009

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

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 (12)

Triviality of fibers for Misiurewicz parameters in the exponential family ⋮ Infinite-dimensional Thurston theory and transcendental dynamics I: infinite-legged spiders ⋮ The dimension paradox in parameter space of cosine family ⋮ Homotopy Hubbard trees for post-singularly finite exponential maps ⋮ Hausdorff measure of the escaping parameter without endpoints is zero for exponential family ⋮ Indecomposable continua in exponential dynamics -- Hausdorff dimension ⋮ Repelling periodic points and landing of rays for post-singularly bounded exponential maps ⋮ A converse landing theorem in parameter spaces ⋮ Classification of escaping exponential maps ⋮ Exponential Thurston maps and limits of quadratic differentials ⋮ A landing theorem for periodic rays of exponential maps ⋮ The Hausdorff dimension of directional edge escaping points set

Cites Work

• Dynamical properties of some classes of entire functions
• The dynamical fine structure of iterated cosine maps and a dimension paradox
• A combinatorial classification of postsingularly finite complex exponential maps
• Hyperbolic components in exponential parameter space
• Iteration of exponential functions
• HAIRS FOR THE COMPLEX EXPONENTIAL FAMILY
• Dynamics of exp (z)
• Dynamics of entire functions near the essential singularity
• The Differentiability of the Hairs of exp(Z)
• Hausdorff dimension of the hairs without endpoints for λ exp z
• Structural Instability of Exponential Functions
• Hausdorff dimension of theM-set of λ exp(z)
• Dynamics of the family 𝜆tan𝑧
• LIMITING DYNAMICS FOR THE COMPLEX STANDARD FAMILY
• ESCAPING POINTS OF EXPONENTIAL MAPS
• Dynamical convergence of polynomials to the exponential
• Classification of escaping exponential maps
• Hausdorff dimension of exponential parameter rays and their endpoints
• A landing theorem for periodic rays of exponential maps
• Topological dynamics of exponential maps on their escaping sets

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