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arXiv · 0908.0723

A renormalization fixed point for Lorenz maps

Björn Winckler
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Abstract

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.

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Björn Winckler. 2010-03-14. A renormalization fixed point for Lorenz maps. https://doi.org/10.1088/0951-7715%2F23%2F6%2F003

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