naa a22 4500 510781640 CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130801xx s 000 0 eng 10.1007/s11854-013-0021-2 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0021-2 Baker's conjecture and Eremenko's conjecture for functions with negative zeros [Elektronische Daten] [P. Rippon, G. Stallard] We introduce a new technique that allows us to make progress on two long standing conjectures in transcendental dynamics: Baker's conjecture that a transcendental entire function of order less than 1/2 has no unbounded Fatou components, and Eremenko's conjecture that all the components of the escaping set of an entire function are unbounded. We show that both conjectures hold for many transcendental entire functions whose zeros all lie on the negative real axis, in particular those of order less than 1/2. Our proofs use a classical distortion theorem based on contraction of the hyperbolic metric, together with new results which show that the images of certain curves must wind many times round the origin. Hebrew University Magnes Press, 2013 Rippon P. Department of Mathematics and Statistics, The Open University, Walton Hall, MK7 6AA, Milton Keynes, UK aut Stallard G. Department of Mathematics and Statistics, The Open University, Walton Hall, MK7 6AA, Milton Keynes, UK aut Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 120/1(2013-08-01), 291-309 0021-7670 120:1<291 2013 120 11854 https://doi.org/10.1007/s11854-013-0021-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0021-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rippon P. Department of Mathematics and Statistics, The Open University, Walton Hall, MK7 6AA, Milton Keynes, UK aut NATIONALLICENCE 700 1- Stallard G. Department of Mathematics and Statistics, The Open University, Walton Hall, MK7 6AA, Milton Keynes, UK aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 120/1(2013-08-01), 291-309 0021-7670 120:1<291 2013 120 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer