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.
Original language | English |
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Article number | 112701 |
Number of pages | 18 |
Journal | Journal of Mathematical Physics |
Volume | 62 |
Issue number | 11 |
Early online date | 3 Nov 2021 |
DOIs | |
Publication status | Published - 30 Nov 2021 |
Keywords
- dynamical systems
- renormalisation group
- universality
- period-doubling
- bifurcations
- computer-assisted proofs