Sixth Framework Programme

Marie Curie Actions

 

EU Research Training Network CODY

Conformal Structures and Dynamics

Research Training Networks
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Recruitment

Vacancy Details ESR position Warwick (ref 1)

(see also the vacancy on the EU CORDIS webpage)

Contract Number
035651
Core Project Title
Conformal Structures and Dynamics
Job Title
Ph.D. position in Dynamical Systems (Filled)
Job Description

A classical theorem by Denjoy asserts that every C^2 circle diffeomorphism with irrational rotation number (i.e. without periodic points) does not have a wandering interval. A consequence is that any C^2 circle diffeomorphism is topologically conjugate to a rigid rotation. Conversely, it was shown that for every epsilon >0, there exist C^(2-epsilon) diffeomorphisms with a wandering interval. Hence, a clear break in the dynamics of circle maps occurs when viewed from the point of smoothness of these maps.

In two dimensions much less is known; simple examples show that certain dynamical phenomena that arise on the circle do not arise on for example the two-torus and vice versa. Even the topology of the wandering domains on the torus has not been systematically studied. There are examples known of diffeomorphisms of class C^(3-epsilon) with that are semiconjugate to a translation, have no periodic points and have a wandering domain with dense orbit. It is conjectured that on the torus the break in possible behaviour occurs at n=3. That is, there are no wandering domains possible for C^3 maps from the torus to itself.

There are some analogies of the nonlinearity and Schwarzian derivative cocycle in higher dimension. The project aims to investigate whether these are of use in studying problems of the kind mentioned above.

Contract Type
temporary
Position
Early Stage Researcher (max. 4 years of research experience)
Number of Positions
1
Deadline
01/01/2007
Start Date
01/01/2007
Duration
30 months
How to apply
Email
Contact Person

Professor Sebastian van Strien
Email: strien@maths.warwick.ac.uk
Homepage : http://www.maths.warwick.ac.uk/~strien/

City
Coventry
Country
United Kingdom
Place Of Work
Organisation City Country
University of Warwick Coventry United Kingdom
Disciplines
Mathematics:   Chaos theory, Geometry, Mathematical analysis