Rare Events for Dynamical Systems via Transfer Operator Techniques PhD

Mathematical Sciences
Entry requirements:
3 years
not available
Reference number:
Start date:
01 October 2018
Is funding available?
UK/EU fees:
International fees:
Application deadline:
16 February 2018



of research classed as 'internationally recognised'

REF 2014


in the UK for Mathematics

The Complete University Guide 2018


Loughborough University is a top-ten rated university in England for research intensity (REF2014) and an outstanding 66% of the work of Loughborough’s academic staff who were eligible to be submitted to the REF was judged as ‘world-leading’ or ‘internationally excellent’, compared to a national average figure of 43%.

In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career. 

Project detail

The research will be conducted in the Department of Mathematical Sciences which works to deliver innovative research that has the potential to have significant impact on industry.   Nonlinear dynamics is one of the main research themes in the Department.  This includes integrable systems, dynamical systems, ergodic theory, stochastic systems, nonlinear PDEs, biological systems, waves and vortices in geophysical fluid dynamics. Research students within the department enjoy a vibrant learning community benefitting from a range of resources to support their work, plus the opportunity to undertake training in lecturing/tutoring.

The study of rare events in dynamical systems is currently one of the most active branches of research in ergodic theory. In part, this is due to their interesting applications in earth and ocean sciences. An example of a rare event in dynamical systems appears in the study of ‘open’ systems where orbits infrequently escape from the domain, typically by falling into a small “hole” in the phase space. The goal of the project is to use spectral techniques (via the so called Perron-Frobenius operator) to approximate escape rates in open systems and to compute the Hausdorff dimension of survival sets.


Primary supervisor: Dr Wael Bahsoun

Secondary supervisor:  Dr Brian Winn

Find out more

For further project details email Dr Wael Bahsoun or register your interest and ask us a question.

To find out more about postgraduate research in the School of Science please visit our website.

Entry Requirements

Applicants should have, or expect to achieve, a 1st or 2:1 Honours degree (or equivalent) in Mathematics or a related subject. A relevant Master’s degree will be an advantage.

Applicants must meet the minimum English Language requirements, details available on the website.

Fees and funding


Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Special arrangements are made for payments by part-time students.

This studentship will be awarded on a competitive basis to applicants who have applied to this project and/or any of the advertised projects prioritised for funding by the School of Science.

The 3-year studentship provides a tax-free stipend of £14,553 (2017 rate) per annum (in line with the standard research council rates) for the duration of the studentship plus tuition fees at the UK/EU rate.  International (non-EU) students may apply however the total value of the studentship will be used towards the cost of the International tuition fee in the first instance.

How to apply

All applications should be made online. Under programme name, select ‘Mathematical Sciences’.

Please quote reference number: WB/MA/2018

Application details

Reference number:  WB/MA/2018
Start date: 01 October 2018
Application deadline: 16 February 2018