UK Nonlinear News, February 1998

Current Activity in Dynamical Systems at the University of Warwick

By Sebastian van Strien

The following activities will be of interest to readers of UK Nonlinear News

  1. Seminars.
  2. Learning Seminars.
  3. Workshop on real and complex one-dimensional systems.
  4. Lectures and Reading Course.
  5. Visitors.
  6. Grant.


Seminars take place on Tuesdays between 3.15 and 4.15pm. The talks are organised by Peter Walters and start Tuesday, 20 January.

Tuesday, 20 January Hans Crauel (Berlin)
Tuesday, 27 January Nikos Fotiades (Greece)
Topological conjugacies of piecewise monotone interval maps
Friday, 30 January A. Katok (Penn State)
Tuesday, 3 February Edson Vargas (San Paulo)
Decay of geometry in the cubic family

Learning Seminars

A more informal seminar, with plenty of questions and talks about unfinished work, results of others and so on, will take place on Tuesdays between 2.00-3.00pm.

Tuesday, 13 January Torsten Fischer
Introduction to coupled map lattices and transfer operators.
Tuesday, 20 January TBA
Tuesday, 27 January TBA

Workshop on Real and Complex One-Dimensional Systems

This term a number of people will discuss some results on Mandelbrot sets. This will take place on Wednesdays, between 3.00-5.00pm. Those involved includes: Tan Lei, Sebastian van Strien, Stefano Luzzatto and Filipe Gonzales. The first meeting is on Wednesday, 14 January.

Lectures and Reading Course

Sebastian van Strien will give a series of talks on Genericity of hyperbolicity of one-dimensional dynamical systems. A very old conjecture by Fatou states that the set of parameters for which a rational map of a given degree is hyperbolic is dense (in the parameter space). Recently, this conjecture has been solved in the special setting of maps of the form z2+c with c real, by Graczyk and Swiatek (Annals, last issue 1997) and Lyubich (Acta Math., vol.178, 1997). Sebastian will give a sketch of the proofs during these lectures, and everybody is welcome. Interested students can also take a reading course on this exciting subject.

The talks take place on Thursdays in Room 123 between 2.00-3.00pm, starting on Thursday 15 January.


Edson Vargas (San Paulo) 20 January, 2 weeks (contact Sebastian)
Nikos Fotiades (Greece) 21 January, 10 days (contact Sebastian)
Ben Mestel (Exeter) 3 months
Lai Sang Young (UCLA) April, a week or so
Colin Sparrow (Cambridge) April-July


Grant money is available from the Alliance: for cooperation between Warwick and Orsay. It seems that Benedicks (Technical University, Stockholm), Sebastian van Strien and Stefano Luzzatto have been given permission to go ahead with their European Programme, Probabilistic Methods in Dynamical Systems. A first meeting is scheduled to take place early May.

Sebastian van Strien (

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