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arXiv · 2006.13127

Rigorous computer-assisted bounds on the period doubling renormalisation fixed point and eigenfunctions in maps with critical point of degree 4

Andrew D Burbanks·Andrew H Osbaldestin·Judi A Thurlby
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Abstract

We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of unimodal maps with degree $4$ critical point. We use a contraction mapping argument to bound essential eigenfunctions and eigenvalues for the linearisation of the operator and for the operator controlling the scaling of added noise. Multi-precision arithmetic with rigorous directed rounding is used to bound operations in a space of analytic functions yielding tight bounds on power series coefficients and universal constants to over $320$ significant figures.

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Andrew D Burbanks, Andrew H Osbaldestin, Judi A Thurlby. 2020-06-23. Rigorous computer-assisted bounds on the period doubling renormalisation fixed point and eigenfunctions in maps with critical point of degree 4. https://doi.org/10.1063/5.0054823

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