11 citations · 43 across the 9 of their papers we have counts for
9 papers
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…
Phenomena of complex analytic dynamics in the systems of alternately excited coupled non-autonomous oscillators and self-sustained oscillators
O. B. Isaeva, S. P. Kuznetsov, A. H. Osbaldestin
A feasible model is introduced that manifests phenomena intrinsic to iterative complex analytic maps (such as the Mandelbrot set and Julia sets). The system is composed of two coup…
Directed current in the Holstein system
D. Hennig, A. D. Burbanks, A. H. Osbaldestin
We propose a mechanism to rectify charge transport in the semiclassical Holstein model. It is shown that localised initial conditions, associated with a polaron solution, in conjun…
Emergence of continual directed flow in Hamiltonian systems
D. Hennig, A. D. Burbanks, C. Mulhern +1
We propose a minimal model for the emergence of a directed flow in autonomous Hamiltonian systems. It is shown that internal breaking of the spatio-temporal symmetries, via localis…