UK Nonlinear News, November 1998.


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UK Nonlinear News

Snapshots of a Lively Character: Mary Lucy Cartwright, 1900-1998

Philip J. Davis reminisces about Mary Cartwright from the perspective of a decades-long friendship, appreciating her especially for a ``mind and a tongue sharpened over the years by the repartee of Oxbridge high table wits.'' The article appears in SIAM News, Volume 31(6), July/August 1998, 4.

UK Nonlinear News ran a news item on Topological Methods in ODE's: The Mathematical Collaboration of M.L. Cartwright and J.E. Littlewood in a previous issue.

50 Years since the world's first stored-program computer ran

In 1948, the world's first stored-computer performed its first (dramatic) computation at the University of Manchester; this Spring, researchers gathered at Manchester to celebrate 50 years of progress in computers and numerical analysis

SIAM News 31(7), September 1998.

The lead article in SIAM News 31(7) is a report on this conference, co-sponsored by the UK and Republic of Ireland (UKIE) SIAM Section. Slides from some of the talks and photographs are available at".

``Computer Simulation and Beyond --- for the 21st Century"

In Notices of the American Mathematical Society 45(9), October 1998, pages 1120-1123, John Guckenheimer discusses the need for a broadening in the scope of the mathematical theories that provides the foundations for the analysis of computer simulations. Many of the scientific problems that computer simulation are increasingly been used for are not readily modelled using the approach that has been so successful in dealing with fluid mechanics. New mathematical theories are required in order to ensure that these complex problems can be tackled efficiently.

Guckenheimer discusses five issues that will present challenges to twenty-first century mathematics:

RESEARCH-EXPOSITORY SURVEY: Symbolic dynamics and Markov partitions

ABSTRACT. The decimal expansion of real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history through a partition. But in order to get a useful symbolism, one needs to construct a partition with special properties. In this work we develop a general theory of representing dynamical systems by symbolic systems by means of so-called Markov partitions. We apply the results to one of the more tractable examples: namely, hyperbolic automorphisms of the two dimensional torus. While there are some results in higher dimensions, this area remains a fertile one for research.

Roy L. Adler, Bulletin (New Series) of the American Mathematical Society 35(1), January 1998, 1-56.

The universal templates of Ghrist

ABSTRACT. This is a report on recent work of Robert Ghrist in which he shows that universal templates exist. Put another way, there are many structurally stable flows in the 3-sphere, each of which has periodic orbits representing every knot type. This answers a question raised originally by Mo Hirsh and popularized by the contrary conjecture by John Birman and the present author.

R.F. Williams, Bulletin (New Series) of the American Mathematical Society 35(2), April 1998, 145-156.

Nonlinearity offers multimedia features to authors

Nonlinearity now offers multimedia features to authors. The Paper "Bifurcations of periodic orbits with spatio-temporal symmetries" by A.M. Rucklidge and M. Silber published in Nonlinearity 11(5) includes two animations (each in both Animated GIF and MPEG formats) showing alternating rolls in 3-D compressible magnetoconvection.

Source: Samantha Trafford (

Nonlinearity 11(5): Table of Contents

Nonlinearity 11(5), September 1998, 1185-1456.
1185 A renormalization group for Hamiltonians: numerical results.
J.J. Abad, H. Koch and P. Wittwer
1195 Singular normal form for the Painlevé equation P1.
O. Costin and R.D. Costin
1209 Beyond the periodic orbit theory.
P. Cvitanovi\'c, K. Hansen, J. Rolf and G. Vattay
1233 Bifurcation structures in maps of Hénon type.
K.T. Hansen and P. Cvitanovi\'c
1263 Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points.
R. Zweim\"{u}ller
1277 The Ginzburg--Landau equation III. Vortex dynamics.
Yu N. Ovchinnikov and I.M. Sigal
1295 Long-time behaviour of Ginzburg--Landau vortices.
Yu N. Ovchinnikov and I.M. Sigal
1311 CP2 soliton scattering: the collective coordinate approximation.
J. Burzlaff and W.J. Zakrzewski
1321 Anomalous transport in a model of Hamiltonian round-off.
J.H. Lowenstein and F. Vivaldi
1351 Random perturbations of chaotic dynamical systems: stability of the spectrum.
M. Blank and G. Keller
1365 Geometry of Kapitsa's potentials.
M. Levi
1369 Attractors for non-compact semigroups via energy equations.
I. Moise, R. Rosa and Xiaoming Wang
1395 Orbital measures in non-equilibrium statistical mechanics: the Onsager relations.
L. Rondoni and E.G.D. Cohen
1407 Fronts and interfaces in bistable extended mappings.
R. Coutinho and B. Fernandez
1435 Bifurcations of periodic orbits with spatio-temporal symmetries.
A.M. Rucklidge and M. Silber

Source: Samantha Trafford (

Nonlinearity 11(6): Table of Contents

Nonlinearity 11(6), November 1998, 1457-1676.
1457 The two loop soliton solution of the Vakhnenko equation
V.O. Vakhnenko and E.J. Parkes
1465 Nonlinear stability around an elliptic equilibrium point in a Hamiltonian system
L. Niederman
1481 Instability in Fermi--Ulam `ping-pong' problem
V. Zharnitsky
1489 Global existence and uniqueness for an optical fibre laser model
A. Mielke, P. Holmes and J.N. Kutz
1505 Global study of a family of cubic Li\'enard equations
A.I. Khibnik, B. Krauskopf and C. Rousseau
1521 Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
E. Horozov and I.D. Iliev
1539 Localized solutions in lattice systems and their bifurcations caused by spatial interactions
L.A. Bunimovich and D. Turaev
1547 The numerical integration of relative equilibrium solutions. Geometric theory
A. Duràn and J.M. Sanz-Serna
1569 Resonances in a spring-pendulum: algorithms for equivariant singularity theory
H.W. Broer, I. Hoveijn, G.A. Lunter and G. Vegter
1607 Billiard systems in three dimensions: the boundary integral equation and the trace formula
M. Sieber
1625 On the vanishing viscosity limit for the 2D incompressible Navier--Stokes equations with the friction type boundary conditions
T. Clopeau, A Mikeli\'c and R. Robert
1637 Stability and persistence of relative equilibria at singular values of the moment map
E. Lerman and S.F. Singer
1651 Breathers in the weakly coupled topological discrete sine-Gordon system
M. Haskins and J.M. Speight
1673 Author index with titles

Source: Katie Pennicott (

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Last updated: 1st November 1998.