Return time statistics and rates of mixing for linked twist maps (SUSTech candidates only)


Please contact Professor Robert Sturman (Leeds) or Professor Zhihong Xia (SUSTech) to discuss this project further informally. 

Project description

Linked twist maps are a non-uniformly hyperbolic generalisation of the well-known Arnold Cat Map. They form a (very simplistic, but fundamental) model of uid mixing devices, where a good mixing region is surrounded by boundaries which inhibit the mixing. A detailed understanding of the mixing behaviour of such maps is therefore desirable. Asymptotic results on mixing rates, measured with decay of correlations, are known in the simplest toral case, an argument which uses the Young Tower argument.

This project could (i) adapt the same argument in the geometrically more complicated, but more applicable, planar case; (ii) use return time statistics to build a more detailed understanding of the mixing process, using a combination of knowledge of the detailed behaviour of LTMs and non-uniform hyperbolicity, rigorous understanding of return time statistics, phenomenological argument and numerical investigation.

Entry requirements

Applicants should have, or expect to obtain, a minimum equivalent of a UK upper second class honours degree in Mathematics or a related discipline.

How to apply

If English is not your first language, you must provide evidence that you have English language proficiency of at least IELTS 6.5 with no component below 6.0, or equivalent.

Applications should be submitted via SUSTech in the first instance. Following nomination by SUSTech, formal applications for Split-site research degree study should then be made online through the University of Leeds website.  Please state clearly in the research information section that the PhD you wish to be considered for is ‘Return time statistics and rates of mixing for linked twist maps (SUSTech candidates only)’ as well as Professor Rob Sturman as your proposed supervisor.

If you require any further information please contact the Graduate School Office e: