STAFF
HONORARY STAFF
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PROFESSOR SEBASTIAN VAN STRIEN
Chair in Dynamical Systems
Phone: +44(207)59-42844
Room: 6M36 Huxley Building
PUBLICATIONS
FURTHER INFO
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Sebastian van Strien
Dynamics of Learning and Iterated Games (2023-2024, 1st term)
Other Teaching Material
MSc Projects
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Numerical calculation of topological entropy for one-dimensional maps.
Topological entropy is a measure of the dynamical complexity of a dynamical systems.
There are quite a few algorithms for computing topological entropy,
but most of them are not very effective. In the case of dynamical
systems in dimension one, the situation is better, but there is an
obvious gap in the literature. This project aims to fill this gap, and ie expected to result in a publication in an international journal (jointly with supervisor).
About one third of the project will consist of reading the literature,
and then to implement some algorithms in computer code.
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Game dynamics.
During the last decades there has been a constant interest in the dynamics
of games, in particular in so called replicator dynamics but also in
some other classes of dynamical systems associated to games. This
project will explore connections between different types of game
dynamics and investigate some research questions. The first part of
this project will involve reading some recent papers in depth. Depending on the strengths and interests of the student, the project then will continue a more mathematical and numerical approach.
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Renormalisation
The aim of this project is to go through a recent proof of the
Feigenbaum-Coullet-Tresser renormalisation conjectures, of
universality in period doubling. These results belong to some of the
most remarkable that were obtained in the field of dynamical systems.
Current proofs rely on hyperbolic geometry, Teichmuller theory and
so-called complex bounds. The project will consist of learning the
background material for these proofs, and going through a recent Annals of Mathematics paper by Avila and Lyubich. This project will be an excellent preparation for doing a PhD in dynamical systems and is more on the pure side.
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Other projects on low-dimensional dynamics or game dynamics, suggested
by students are also most welcome.
Summer Projects (examples)
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