A number of PhD studentships are funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership with Exeter to commence in September 2017. The projects are funded on a competitive basis. Usually the projects that receive the best applicants will be awarded the funding. The studentships will provide funding for a stipend which, is currently £14,296 per annum for 2016-2017, research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

The link to the list of projects is here (note that the list is long, applied maths & dynamics projects are mixed with others):

http://www.exeter.ac.uk/postgraduate/research-degrees/mathematics/funding/

A 3-year position as a Postdoctoral Research Fellow is available  in the research group (working with Jan Sieber:

http://www.jobs.ac.uk/job/AUU269/postdoctoral-research-fellow/

Also, internationally, several tenure track/permanent positions are open:

McGill (tenure track, info from Tony Humphries):
http://www.mathjobs.org/jobs/jobs/9249
DTU Lyngby (permanent, info from Frank Schilder):
http://www.compute.dtu.dk/om_os/ledige_stillinger/job?id=4778215b-b1f1-4a38-b927-666abf94cbb8