Corpus ID: 118449377

Complex box bounds for real maps

@article{Clark2013ComplexBB,
  title={Complex box bounds for real maps},
  author={Trevor Clark and Sebastian van Strien and Sof{\'i}a Trejo},
  journal={arXiv: Dynamical Systems},
  year={2013}
}
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 to such a map a complex box mapping (which provides a kind of Markov structure), together with universal geometric bounds on the shape of the domains. Such bounds show that the first return maps to these domains are well-controlled, and consequently form one of the corner stones in many recent results on one-dimensional dynamics: renormalisation… Expand
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