A renormalization fixed point for Lorenz maps

Details A renormalization fixed point for Lorenz maps A renormalization fixed point for Lorenz maps

2009-08-05

arxiv.org/abs/0908.0723v2

Mathematics

Dynamical Systems

29 pages, 2 figures

Scientific paper

A Lorenz map is a Poincar\'e map for a three-dimensional Lorenz flow. We describe the theory of renormalization for Lorenz maps with a critical point and prove that a restriction of the renormalization operator acting on such maps has a hyperbolic fixed point. The proof is computer assisted and we include a detailed exposition on how to make rigorous estimates using a computer as well as the implementation of the estimates.

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