My research is in the area of complex dynamics and concerns the iteration of transcendental meromorphic functions - more details are given below.

I have a long standing interest in the issues surrounding women's careers in mathematics and chaired the London Mathematical Society's Women in Mathematics Committee from 2006 to 2015. This work was recognized by the award of an OBE in 2015. Details of the work of the committee and the activities that it organises to support women's careers can be found here http://www.lms.ac.uk/women-mathematics. I also represented the LMS on the Athena Forum http://www.athenaforum.org.uk/. I continue as a member of the LMS Good Practice Scheme Steering Committee and a member of LMS Council. I chair the School's Athena SWAN self assessment team - we were awarded a Bronze award in 2014.

My research is in the area of complex dynamics and concerns the iteration of transcendental meromorphic functions. I am particularly interested in the possible dimensions of the Julia set and in the structure of the escaping set.

Together with Professor Phil Rippon, I lead the complex dynamics group at the OU. The group currently comprises a Visiting Research Associate and two PhD students and our activities often include other complex analysts in the department.

Phil Rippon and myself are currently working on a project to investigate a surprising link that we identified between two open conjectures in complex dynamics: Baker's conjecture and Eremenko's conjecture. The work has been funded by the EPSRC by two grants which together funded our work for five years (0.5FTE each). More details on the project are given here:

- EP/H006591/1: Baker's conjecture and Eremenko's conjecture: a unified approach
- EP/K031163/1: Baker's conjecture and Eremenko's conjecture: new directions

Our former Research Associate, Dave Sixsmith, was funded by the following grant from the EPSRC:

- EP/J022160/1: Dimensions in complex dynamics: spiders' webs and speed of escape

Most of my teaching has been in the area of analysis. I am currently chair of the exam board for __M208 Pure Mathematics__ and am responsible for the MSc course __M835 Fractal Geometry__.

Name | Type | Parent Unit |
---|---|---|

Pure Maths: Analysis & Geometry Research Group | Group | Faculty of Mathematics, Computing and Technology |

Role | Start date | End date | Funding source |
---|---|---|---|

Lead | 01/Apr/2018 | 31/Mar/2021 | EPSRC EPSRC Engineering and Physical Sciences Research Council |

The main aim of the proposed research is to complete the classification of the types of dynamical behaviour that can occur within the components of the Fatou set (the set of stability) arising in the iteration of analytic functions. There is a large historical body of work classifying the dynamical behaviour within periodic Fatou components and a recent paper gives a complete description of the behaviour in multiply connected wandering domains. This project will address the outstanding case of simply connected wandering domains. There are many different types of dynamical behaviour within such domains and they have not previously been studied systematically. The development of a unifying theory will be fundamental to future work on iteration. The theory will be illustrated and informed by the construction of new examples of wandering domains. |

Nicks, Daniel; Rippon, Philip and Stallard, Gwyneth

International Mathematics Research Notices ((In Press))

Osborne, John W.; Rippon, Philip J. and Stallard, Gwyneth M.

Journal d’Analyse Mathematique, 139(2) (pp. 521-558)

Rippon, Philip and Stallard, Gwyneth

Transactions of the American Mathematical Society, 372(5) (pp. 3083-3111)

Nicks, Daniel A.; Rippon, Philip J. and Stallard, Gwyneth M.

Proceedings of the London Mathematical Society, 117(1) (pp. 100-124)

Rippon, P. J. and Stallard, G. M.

Journal d'Analyse Mathematique, 134(2) (pp. 801-810)

Osborne, John; Rippon, Philip and Stallard, Gwyneth

Ergodic Theory and Dynamical Systems, 37(4) (pp. 1291-1307)

Benini, Anna Miriam; Rippon, Philip J. and Stallard, Gwyneth M.

Advances in Mathematics, 287 (pp. 451-462)

Rippon, P. J. and Stallard, G. M.

Transactions of the American Mathematical Society, 367(1) (pp. 377-399)

Rippon, Philip Jonathan and Stallard, Gwyneth Mary

International Mathematics Research Notices, 2014(19) (pp. 5203-5229)

Rippon, P. J. and Stallard, G. M.

Advances in Mathematics, 244 (pp. 337-353)

Bergweiler, Walter; Rippon, Philip and Stallard, Gwyneth

Proceedings of the London Mathematical Society, 107(6) (pp. 1261-1301)

Rippon, Philip and Stallard, Gwyneth

Proceedings of the London Mathematical Society, 105(4) (pp. 787-820)

Rippon, Philip and Stallard, Gwyneth

Journal d'Analyse Mathematique, 120(1) (pp. 291-309)

Rippon, P. J. and Stallard, G. M.

Proceedings of the American Mathematical Society, 139(8) (pp. 2807-2820)

Rippon, Philip and Stallard, Gwyneth

Transactions of the American Mathematical Society, 363(8) (pp. 4171-4201)

Rempe, Lasse and Stallard, Gwyneth M.

Proceedings of the American Mathematical Society, 138(5) (pp. 1657-1665)

Rempe, Lasse; Rippon, Philip J. and Stallard, Gwyneth M.

Journal of Difference Equations and Applications, 16(5&6) (pp. 739-762)

Bergweiler, Walter; Karpińska, Boguslawa and Stallard, Gwyneth M.

Journal of the London Mathematical Society, 80(3) (pp. 680-698)

Rippon, P. J. and Stallard, G. M.

Journal d’Analyse Mathematique, 108(1) (pp. 61-86)

Rippon, P. J. and Stallard, G. M.

Mathematische Zeitschrift, 261(3) (pp. 557-570)

Bergweiler, W.; Rippon, Philip J. and Stallard, Gwyneth M.

Proceedings of the London Mathematical Society, 97(2) (pp. 368-400)

Rippon, P. J. and Stallard, G. M.

Journal of the London Mathematical Society, 77(2) (pp. 405-423)

Rippon, P.J. and Stallard, G.M.

Ergodic Theory and Dynamical Systems, 26(2) (pp. 525-538)

Rippon, P. J. and Stallard, G. M.

Mathematical Proceedings of the Cambridge Philosophical Society, 141(2) (pp. 371-382)

Rippon, P. J. and Stallard, G. M.

Journal d’Analyse Mathematique, 96 (pp. 225-245)

Rippon, P.J. and Stallard, G.M.

Journal of the London Mathematical Society, 71(3) (pp. 669-683)

Rippon, P.J. and Stallard, G.M.

Proceedings of the American Mathematical Society, 133(4) (pp. 1119-1126)

Stallard, Gwyneth M.

Bulletin of the London Mathematical Society, 36(2) (pp. 263-270)

Stallard, Gwyneth M.

Bulletin of the London Mathematical Society, 33(6) (pp. 689-694)