UK Nonlinear News, August 1997


Conference Announcements

Symmetry in Hamiltonian Dynamics

4-5 September 1997

University of Surrey

Dynamical systems that are encountered in applications often possess symmetries that criticality govern the generic behaviour that can occur in such systems. Therefore, a general theoretical understanding of symmetric dynamical systems is important for many scientific and technical problems. This workshop will consider various aspects of dynamical systems that have a Hamiltonian structure and are equivariant with respect to a Lie Group.

Speakers will include:

This workshop will be held at the Department of Mathematics and Statistics of the University of Surrey and the Centre for Interdisciplinary Nonlinear Mathematics at the University of Surrey and is sponsored by

London Mathematical Society and the School of Electronics, Information Technology and Mathematics.

The workshop will start on Thursday 4 September 1997 in the afternoon with talks from approximately 1:30pm until 6:00pm and continue on Friday 5 September 1997 for a more informal second day.

Some funds are available to support interested participants -- contact the organisers for further information. Further details are available at

Source: Gianne Derks (

Combustion Theory

5th September


In conjunction with the visits of Gregory Sivashinsky and Rod Weber a one-day meeting will be held in UMIST on Combustion Theory, on Friday 5th September 1997. Speakers will include:

Details will be posted under the web page If you are interested in attending or contributing to this meeting please contact Bill Dold ( for further details. Prior notification will be needed if you want to join in the lunch.

Source: Bill Dold (

7th International Conference on Numerical Combustion

30th March to 1st April 1998

St John's College, York

Updated details about this conference are available through the web pages under Key dates to remember are the deadlines for submissions:

minisymposia 1st October, 1997
contributed lectures 1st November, 1997
poster sessions 1st November, 1997

This will be the first SIAM conference to be held in Britain, as a consequence of the creation of the new SIAM (UK and Ireland) section.

Source: Bill Dold (

The ANM Spring School 1997

An outstanding pictorial overview of this meeting is now available at (A report on this meeting also appeared in our last issue - UKNONL)

Source: Andy Osbaldestin (

Dynamics Days '97 cancelled

Dynamics Days '97, planned to take place at Danish Technical University, Copenhagen has been cancelled. Dynamics Days '98 is planned for Edinburgh, contact John Hogan for additional details.

Source: Predrag Cvitanovic (

Last Meeting of the ANM panel

The Applied Nonlinear Mathematics (ANM) panel has met for the last time, in Bristol on 10th July 1997. The programme will be reviewed in the next year or so. Anyone who wishes to put on an ANM Spring school from 1998 onwards can still apply to EPSRC in the usual manner as for any training programme. The closing date for each year is 1 December. The procedure is very simple for what has always been a very popular and rewarding event. Previous Spring school organisers (or John Hogan, can be contacted if a bid is being contemplated.

Source: John Hogan (

New software package: "Interactive Differential Equations"

Steven Strogatz has co-authored a new software package "Interactive Differential Equations" to help in teaching differential equations to undergraduates. It deals with the traditional topics as well as nonlinear systems and chaos, and includes many applications in physics, biology, engineering, mechanics, and chemistry. It has been written to be easy to use.

A preview version of the software is available on the web. Go to and click on the links to "mathematics" and "interactive differential equations". To try the demonstrations click on "demo". When using the demo version keep in mind that the package runs much faster off a CD than over the web!

Source: Steven Strogatz (

Topological Methods in ODE's: The Mathematical Collaboration of M.L. Cartwright and J.E. Littlewood.

The past thirty years has witnessed an explosion of interest in dynamical systems. The impetus for this growth is commonly dated to a landmark survey paper on hyperbolic systems by Smale[1] which outlined a number of outstanding problems. Although initially dynamical systems research was dominated by pure mathematicians over the last twenty years their ideas and tools have found ready applications in the engineering and applied science communities. Yet, although the resurgence in interest in dynamical systems may have stemmed from abstract problems the historical roots of many of these problems are in concrete applied problems.

The origins of modern dynamical systems theory stem is the 19th century interest in celestial mechanics, in particular the motion of the bodies in the solar system. Working on the three-body problem Poincaré anticipated many of the developments that would be pursued in the 20th century. A new book [2] provides a popular account of these developments, together with some biographical details about the scientists and mathematicians who created them.

van der Pol's experiments on electrical circuits during the 1920s and 1930s opened up another chapter in the history of dynamics: his research stimulated mathematical interest in nonlinear oscillations. Some of the earliest rigorous work in the field of large parameter theory was produced by the Cambridge mathematicians Cartwright and Littlewood. They were among the first mathematicians to recognise that topological and analytical methods could be combined to efficiently obtain results for various problems in differential equations, and their results helped inspire the construction of Smale's horseshoe diffeomorphism[3]. An article examining their mathematical collaboration has recently appeared[4].

  1. Smale, S. Differentiable Dynamical Systems. Bull. Amer. Math. Soc. 73, 747-817, 1967.
  2. Diacu, F. and Holmes, P. Celestial Mechanics: The Origin of Chaos and Stability. Princeton University Press.
  3. Smale, S. Differential and Combinatorial Topology, pp 63-80, Princeton, 1965.
  4. McMurran, S.L. and Tattersall, J.J. The Mathematical Collaboration of M.L. Cartwright and J.E. Littlewood. The American Mathematical Monthly, 103:10, 833-845 1996.

TUXEDO: The UK Spatially Extended Dynamics Organisation

TUXEDO (The UK Spatially Extended Dynamics Organisation) has been created by Robert MacKay (Cambridge), David Rand (Warwick) and Paul Glendinning (Queen Mary & Westfield College, London) to exchange results and ideas about the dynamics of spatially extended systems, and stimulate new research and collaboration. The London Mathematical Society is supporting several one-day meetings during the academic year 1997/1998, for researchers from our three respective centres, but we welcome the participation of others. The first meeting is planned for 24 September, 11am - 5pm, at DAMTP in Cambridge. A webpage will be created towards the end of August, to be attached to, so please look there to find further details (but not before 12 August as I'm going to the Dynamical Systems Symposium in Rio and will not have time to make the webpage until I return!).

(A number of EC Postdoctoral Research Fellowships have been awarded to the tuxedo group. Further details are available elsewhere in this issue - UKNONL.)

Source Robert S. MacKay (

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