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| Existence of a period-doubling renormalization fixed point for area-preserving maps of a subset of the plane has been demonstrated in the 80's by J.-P. Eckmann, H. Koch and P. Wittwer using computer-assisted techniques. Since then, the progress towards an analytic proof of this fact has been slow and difficult. We will present an "almost analytic" existence proof which relies on the geometric features of the problem. This is a joint work with P. Hazard. |
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