57 citations · 85 across the 12 of their papers we have counts for
4 papers · 1 filter
Existence of the C-type renormalisation two-cycle
Zainab Rahman, Maria Pickett, Andrew Burbanks
We prove the existence of the C-type renormalisation two-cycle, helping to establish the universality of the C-type route to chaos in families of non-invertible maps of the plane.…
Rigorous computer-assisted bounds on renormalisation fixed point functions, eigenfunctions, and universal constants
Andrew D Burbanks, Andrew H Osbaldestin, Judi A Thurlby
We gain tight rigorous bounds on the renormalisation fixed point function for period doubling in families of unimodal maps with degree 2 critical point. By writing the relevant eig…
Rigorous bounds on the Hausdorff dimension of Feigenbaum attractors
Andrew D Burbanks, Andrew H Osbaldestin, Judi A Thurlby
We calculate rigorous bounds on the Hausdorff dimension of the attractor at the accumulation of the period-doubling cascade for families of maps with quadratic, cubic, and quartic…
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
We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of unimodal maps with degree critical point. We use a contraction mapping argum…