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A renormalization fixed point for Lorenz maps

A Lorenz map is a Poincaré 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.

preprint2010arXivOpen access
Björn Winckler
math.DS
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Björn Winckler

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