Research outputs per year
Research outputs per year
Dr
Accepting PhD Students
PhD projects
Universality and Renormalisation in Dynamical Systems
I am an Associate Professor (Reader) in Applied Mathematics and the Associate Head for Research and Innovation in the School of Mathematics and Physics at the University of Portsmouth in the UK. I am also an Associate Member of the Institute of Cosmology and Gravitation. My main research interests are in nonlinear dynamics.
I completed my PhD at the University of Loughborough, after which I went on to work at Hewlett-Packard's research laboratories in Bristol before taking up Postdoctoral research positions in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge and later in the School of Mathematics at the University of Bristol where I gained a permanent post as Scientific Programmer.
I gave a course of lectures in Part III of the University of Cambridge Mathematics Tripos (Applied) on renormalisation in Dynamical Systems.
I joined the Department of Mathematics at the University of Portsmouth in 2005, and am now a member of the Applied Mathematics Group, becoming Principal Lecturer in 2012, Associate Head for Research and Innovation in 2019, and Associate Professor (Reader) in Applied Mathematics in 2023.
I have been involved in several successful projects on the interface between science and public understanding, including the Mathematics Posters on the London Underground project in 2000, with the Isaac Newton Institute for Mathematical Sciences in Cambridge, and the Dynamics of Spin exhibit at the Royal Society Summer Science Exhibition in London in 2007 and at Techfest (Asia's largest Science and Technology festival) held in Mumbai in 2008. I also co-founded and chaired the Portsmouth Cafe Scientifique.
1. Universality and Renormalisation in Dynamical Systems, Computer-Assisted Proofs in Banach Spaces.
2. Applied Nonlinear Dynamics including Mathematical Oncology (via ODE and DDE models).
3. Nonlinear dynamics in systems of coupled units; localisation, ratchets, collective phenomena, transport in phase space.
In my PhD, I worked under the supervision of Andrew Osbaldestin (Loughborough) and in collaboration with Andreas Stirnemann (Exeter, Edinburgh). I used computer-assisted techniques to explain the universality observed in the breakup of quasiperiodicity (conjugacy to rigid rotation) on the boundary of Siegel discs in complex maps - a prototypical KAM-type scenario. For golden mean rotation number, I used bounds on the fixed point of the corresponding (Fibonacci-type) renormalisation operator to verify the necklace hypotheses of Stirnemann and thereby to give a rigorous proof of conjectures of Widom explaining the universality observed by Manton and Nauenberg.
While at the University of Cambridge I worked with Colin Sparrow (Cambridge), Jeremy Gunawardena (BRIMS, Hewlett-Packard Laboratories) and Roger Nussbaum (Rutgers) on the dynamics of nonexpansive maps, with applications to discrete event systems.
At the University of Bristol I worked with Stephen Wiggins and Holger Waalkens (Bristol), David Farrelly (Utah State), and others, on transport phenomena in Hamiltonian systems, with applications to problems in Physics, Chemistry, and Celestial Mechanics.
More recently, I have continued my work on renormalisation in dynamical systems (with a focus on coupled systems) and have worked with Marianna Cerasuolo (Portsmouth) on mathematical models of prostate cancer.
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This person’s work contributes towards the following SDG(s):
Ph.D., Renormalisation for Siegel Discs (Applied Mathematics), Loughborough University
1 Sept 1993 → 1 Sept 1997
Award Date: 1 Jul 1997
BSc (Hons), Mathematics and Computation, Loughborough University
1 Sept 1990 → 1 Sept 1993
Award Date: 1 Jul 1993
Scientific Programmer (Permanent Post), Postdoctoral Fellow, School of Mathematics, University of Bristol
1 Sept 2001 → 1 Sept 2005
Lectured Mathematical Tripos Part III (Applied), Postdoctoral Research Associate, Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics (DPMMS), University of Cambridge, UK
1 Sept 1998 → 1 Sept 2001
Postdoctoral Fellow, Basic Research Institute in the Mathematical Sciences (BRIMS), Hewlett-Packard Laboratories Europe, Bristol, UK
1 Sept 1997 → 1 Sept 1998
Visiting Fellow, Santa Fe Institute
1 Sept 1995 → 1 Oct 1995
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Burbanks, A. (Creator), Zenodo, 3 Oct 2022
DOI: 10.5281/zenodo.7139006, https://zenodo.org/record/7139006
Dataset
Burbanks, A. (Creator), Cerasuolo, M. (Creator) & Turner, L. (Creator), Zenodo, 7 Sept 2022
DOI: 10.5281/zenodo.7090867, https://zenodo.org/record/7090867
Dataset
Burbanks, A. (Presented paper)
Activity: Participating in or organising an event types › Participation in conference
Burbanks, A. (Chair)
Activity: Participating in or organising an event types › Participation in workshop, seminar, course
Burbanks, A. (Visiting researcher)
Activity: Visiting an external organisation types › Visiting an external academic institution
Burbanks, A. (Chair)
Activity: Participating in or organising an event types › Participation in workshop, seminar, course
Burbanks, A. (Participant)
Activity: Participating in or organising an event types › Participation in workshop, seminar, course