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@article{Rempe:2015:10.1215/00127094-2885764,
author = {Rempe, L and van, Strien S},
doi = {10.1215/00127094-2885764},
journal = {Duke Mathematical Journal},
pages = {1079--1137},
title = {Density of hyperbolicity for classes of real transcendental entire functions and circle maps},
url = {http://dx.doi.org/10.1215/00127094-2885764},
volume = {164},
year = {2015}
}

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TY  - JOUR
AB  - We prove density of hyperbolicity in spaces of (i) real transcendental entirefunctions, bounded on the real line, whose singular set is finite and real and(ii) transcendental self-maps of the punctured plane which preserve the circleand whose singular set (apart from zero and infinity) is contained in thecircle. In particular, we prove density of hyperbolicity in the famous Arnol'dfamily of circle maps and its generalizations, and solve a number of other openproblems for these functions, including three conjectures by de Melo, Salomaoand Vargas.  We also prove density of (real) hyperbolicity for certain families as in (i)but without the boundedness condition; in particular our results apply when thefunction in question has only finitely many critical points and asymptoticsingularities.
AU  - Rempe,L
AU  - van,Strien S
DO  - 10.1215/00127094-2885764
EP  - 1137
PY  - 2015///
SN  - 0012-7094
SP  - 1079
TI  - Density of hyperbolicity for classes of real transcendental entire functions and circle maps
T2  - Duke Mathematical Journal
UR  - http://dx.doi.org/10.1215/00127094-2885764
UR  - http://arxiv.org/abs/1005.4627v3
UR  - https://projecteuclid.org/euclid.dmj/1429282679
UR  - http://hdl.handle.net/10044/1/18910
VL  - 164
ER  -

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ProfessorSebastianvan Strien

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