School of Mathematics
Alan Turing Building
University of Manchester
Manchester M13 9PL
|Room Number:||2.236 Alan Turing Building|
|Telephone:||+44 (0)161 306 8972|
|Fax:||+44 (0)161 200 3669|
|Research | Publications | Teaching | Graduate Students | EPSRC Reports|
|Links: Academic or Personal | SASHA and SULA | View from the Pennines|
I am a Professor of Applied Mathematics, having previously held chairs in UMIST and Queen Mary, University of London (the photo shows me discussing something vitally important with Jaroslav Stark who sadly died in 2010. I am co-editor of a special issue of Dynamical Systems an International Journal deedicated to his memory. You can find another photo of me on Nick Gilbert and Marc Atkins' Faces of Mathematics home page -- this forms part of an EPSRC project a few years ago.
If you are thinking of doing a Ph.D. with me then you should get an application form from our Postgraduate pages. It is also a good idea to email me so that we can talk about what you might do.
You can find more details of the people
I work with and my academic career.
Some of my papers (and a list of other papers)
are also available. I also have some
personal links. Recent papers can be downloaded
from the departments eprint server.
My current work here focusses on bifurcations from trajectories of differential equations which extend to infinity (examples are the Falkner-Skan equations and the Nose equations). These are still very poorly understood except on an example by example basis. Much of this work is in collaboration with Sir Peter Swinnerton-Dyer at the Newton Institute in Cambridge.
Identical, globally coupled systems can have synchronized states in which every system behaves identically. Bifurcation curves corresponding to bifurcations in which typical chaotic synchronized solutions become unstable may be extremely complicated (fractal). This is associated with blowout bifurcations from the synchronized state (the loss of transverse stability of atypical sychnronized states embedded in the chaotic attractor) in ways which are not completely understood.
It may seem surprising, but there is still a fair amount we do not know about maps as simple as x goes to rx(1-x) with r>0.
Computer simulations of the behaviour of quasi-periodically forced systems suggest that very wierd things can happen (strange non-chaotic attractors, for example). We have been trying to understand different features of these systems, both for maps (with groups in Germany, USA and London) and for flows. The picture shows an example -- as a parameter is changed by a small amount two stable curves collide with an unstable curve to create what appears to be a strange non-chaotic attractor. We don't know whether this is really what is going on, but it is interesting to speculate.
This picture shows the Mandelbrot set for the complex quadratic map. It has almost nothing to do with my research (except insofar as it is a representation of the parameter space of a low dimensional map) but you have to admit that it is pretty. I stole this image from Robert Devaney's Fractal Site.
Course materials for this course are available through the Blackboard system.
Course materials for this course are available through the central School pages and the university Blackboard system.
Last up-dated Feb 2012.