The exponential map is not recurrent

DOI10.1007/BF01162349zbMath0595.30033MaRDI QIDQ1077581

Mary Rees

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173703

zbMATH Keywords

exponential mapiteraterecurrent

Mathematics Subject Classification ID

Topological dynamics (37B99) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Ergodic theory (37A99)

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Iteration of meromorphic functions ⋮ Measurable dynamics of $S$-unimodal maps of the interval ⋮ Limit functions of discrete dynamical systems ⋮ The dynamical fine structure of iterated cosine maps and a dimension paradox ⋮ Measurable dynamics of the exponential map ⋮ On the dynamics of entire functions on the Julia set ⋮ Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces ⋮ Non-recurrence of \(\exp(z)/z\) ⋮ Julia set of \(\lambda \exp(z)/z\) with real parameters \(\lambda\) ⋮ Typical behavior of the trajectories of transformations of a segment ⋮ Most of the maps near have empty Fatou sets ⋮ Most of the Maps near the Exponential are Hyperbolic ⋮ Indecomposable continua in exponential dynamics -- Hausdorff dimension ⋮ Transitive maps which are not ergodic with respect to Lebesgue measure ⋮ Hausdorff dimension and conformal measures of Feigenbaum Julia sets ⋮ Hausdorff dimension of a dynamically defined set of exp(z)/z ⋮ Random non-hyperbolic exponential maps ⋮ Lebesgue measure of Feigenbaum Julia sets ⋮ Limit functions of iterates of entire functions on parts of the Julia set ⋮ Perturbing Misiurewicz parameters in the exponential family ⋮ Geometry and ergodic theory of non-hyperbolic exponential maps ⋮ Dynamical properties of some classes of entire functions

Cites Work

• Repulsive fixpoints of entire functions
• Iteration of exponential functions
• On iterates of e^z
• On the measurable dynamics of z → e^z