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@article{Clark:2017:10.1007/s00220-017-2958-y,
author = {Clark, T and van, Strien S and Trejo, S},
doi = {10.1007/s00220-017-2958-y},
journal = {Communications in Mathematical Physics},
pages = {1001--1119},
title = {Complex box bounds for real maps},
url = {http://dx.doi.org/10.1007/s00220-017-2958-y},
volume = {355},
year = {2017}
}

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TY  - JOUR
AB  - In this paper we prove complex bounds, also referred to as a priori bounds,for real analytic (and even C3) interval maps. This means that we associate tosuch a map a complex box mapping (which provides a kind of Markov structure),together with universal geometric bounds on the shape of the domains. Suchbounds show that the first return maps to these domains are well-controlled,and consequently form one of the corner stones in many recent results onone-dimensional dynamics: renormalisation theory, rigidity results, density ofhyperbolicity, local connectivity.
AU  - Clark,T
AU  - van,Strien S
AU  - Trejo,S
DO  - 10.1007/s00220-017-2958-y
EP  - 1119
PY  - 2017///
SN  - 0010-3616
SP  - 1001
TI  - Complex box bounds for real maps
T2  - Communications in Mathematical Physics
UR  - http://dx.doi.org/10.1007/s00220-017-2958-y
UR  - http://arxiv.org/abs/1310.8338v3
UR  - http://hdl.handle.net/10044/1/48271
VL  - 355
ER  -

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ProfessorSebastianvan Strien

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