Entropy of transcendental entire functions
نویسندگان
چکیده
منابع مشابه
Hausdorff Dimensions of Escaping Sets of Transcendental Entire Functions
Let f and g be transcendental entire functions, each with a bounded set of singular values, and suppose that g ◦ φ = ψ ◦ f , where φ, ψ : C → C are affine. We show that the escaping sets of f and g have the same Hausdorff dimension. Using a result of the second author, we deduce that there exists a family of transcendental entire functions for which the escaping set has Hausdorff dimension equa...
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We prove an analog of Böttcher’s theorem for transcendental entire functions in the Eremenko-Lyubich class B. More precisely, let f and g be entire functions with bounded sets of singular values and suppose that f and g belong to the same parameter space (i.e., are quasiconformally equivalent in the sense of Eremenko and Lyubich). Then f and g are conjugate when restricted to the set of points ...
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We partition the fast escaping set of a transcendental entire function into two subsets, the maximally fast escaping set and the non-maximally fast escaping set. These sets are shown to have strong dynamical properties. We show that the intersection of the Julia set with the non-maximally fast escaping set is never empty. The proof uses a new covering result for annuli, which is of wider intere...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2019
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2019.65