Dynamics of Permutable Transcendental Entire Functions
نویسندگان
چکیده
منابع مشابه
Permutable Entire Functions Satisfying Algebraic Differential Equations
We show that if f and g are transcendental entire functions such that f(g) = g(f), then f satisfies an algebraic differential equation if and only if g does.
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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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Complex dynamics of iterated entire holomorphic functions is an active and exciting area of research. This manuscript collects known background in this field and describes several of the most active research areas within the dynamics of entire functions. Complex dynamics, in the sense of holomorphic iteration theory, has been a most active research area for the last three decades. A number of i...
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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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The basic results of the iteration theory of rational and entire functions used in this paper are contained in the classical papers [10,11], in the survey [5] and in [15, Appendix III]. Let / b e a rational or entire function and let/" = /o . . . o /be its «th iterate. Denote by Jf(f) the set of normality of/ that is, the maximal open set on which the family of iterates is normal in the sense o...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2006
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181069360