Bishop's qc-folding and wandering domains in Eremenko ... - ICMS

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Bishop’s QC-folding for entire maps in class B Important remarks about φ: φ is conformal on S + and 1 4 D k’s. φ is uniformly K-quasiconformal for all the values of λ and d k ’s. The dilatation of φ is supported inside T (r 0 ) and this neighborhood decays exponentially in |z|. Moreover φ is symmetric (1-to-1 on R), φ(0) = 0, φ(∞) = ∞ and φ(z) = z + a z + O ( |z −2 | ) for some |z| > R (Dyn’kin’s Theorem). φ ′ should be bounded by below from 0. Estimates get better when increasing the parameters. Wandering domains and Bishop’s folding
Bishop’s QC-folding for entire maps in class B C S k D k π z k π 2 0 R 1 2 S + Consequently: f ′ (x) = d dx cosh (λ sinh(φ(x))) ≥ 16x for λ large enough. Hence we may choose λ so that x n = f n ( 1 2) tends to infinity (exponential speed) as n does. Wandering domains and Bishop’s folding
Page 1 and 2: Bishop’s qc-folding and wandering
Page 3 and 4: Background Definition: Let f be a r
Page 5 and 6: Wandering domain example II (Herman
Page 7 and 8: Critically finite entire transcende
Page 9 and 10: Composite entire functions and Carl
Page 11 and 12: Eremenko-Lyubich class and wanderin
Page 13 and 14: Bishop’s QC-folding for entire ma
Page 25: Bishop’s QC-folding for entire ma
Page 35: The end!! Thank you!! Wandering dom

Bishop's qc-folding and wandering domains in Eremenko ... - ICMS

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