UK Nonlinear News, November 2002.


Centennial History of Hilbert's 16th Problem

ABSTRACT. The second part of Hilbert's 16th problem deals with polynomial differential equations in the plane. It remains unsolved even for quadratic polynomials. There were several attempts to solve it that failed. Yet the problem inspired significant progress in the geometric theory of planar differential equations, as well as bifurcation theory, normal forms, foliations and some topics in algebraic geometry. The dramatic history of the problem, as well as related, developments, are presented.
Yu. Ilyashenko. Centennial History of Hilbert's 16th Problem. Bulletin (New Series) of the American Mathematical Society 39(3):301-354, 2002.

New Journal: Nonlinear Dynamics and Systems Theory

In March 2001, Academic Periodical Press (National Academy of Sciences of Ukraine) started the publication of a new Journal Nonlinear Dynamics and Systems Theory. The Journal published twice per year in the months of June and December. The preface to the Journal is available at For further details on this journal contact Arkadiy Tyshenko (

Source: Arkadiy Tyshenko (

Special issue: Discrete and Continuous Dynamical Systems celebrates Mark Vishik's 80th birthday

To celebrate the 80th birthday of Professor Mark Vishik who made fundamental contributions to dynamical systems, the journal Discrete and Continuous Dynamical Systems is to devote a special volume consisting of invited contributions from the leading mathematicians and scientists working in this broad field.

Guest Editors: V. Chepyzhov, M. Efendiev, Alain Miranville, and Roger Temam .

Committed Contributors:

Source: Shouchuan Hu (

Table of Contents: Nonlinearity Volume 15(5), September 2002

All articles are free for 30 days after publication on the web.

Nonlinearity, 15(5), September 2002
1379 Area preserving flows with a dense orbit
H. Marzougui
1385 On the stability of some periodic orbits of a new type for twist maps
S. Addas-Zanata and C. Grotta-Ragazzo
1399 On the existence of a new type of periodic and quasi-periodic orbits for twist maps of the torus
S. Addas-Zanata
1417 Orbit bifurcations and wavefunction autocorrelations
A. Bäcker, J.P. Keating and S.D. Prado
1435 Modules of the Abelian integrals and the Picard - Fuchs systems
D. Novikov
1445 Homoclinic tangencies and dominated splittings
L. Wen
1471 Unstable manifolds and Schrödinger dynamics of Ginzburg - Landau vortices
O. Lange and B.J. Schroers
1489 Bogomolny Yang - Mills - Higgs solutions in (2+1) anti-de Sitter space
T. Ioannidou
1499 Sparseness of nonlinear coupling: importance in sparse direct-interaction perturbation
S. Goto and S. Kida
1521 On the spectrum of Farey and Gauss maps
S. Isola
1541 Spectral statistics of rectangular billiards with localised perturbations
S. Rahav and S. Fishman
1595 Entropy of interval maps via permutations
C. Bandt, G. Keller and B. Pompe
1603 Homoclinic orbits of invertible maps
J.M. Bergamin, T. Bountis and M.N. Vrahatis
1621 The optimal interface profile for a non-local model of phase separation
M. Cassandro, E. Orlandi and P. Picco
1653 An elementary construction of complex patterns in nonlinear Schrödinger equations
M. del Pino, P. Felmer and K. Tanaka
1673 Semihyperbolic entire functions
W. Bergweiler and S. Morosawa
1685 Multiscale correction to solitary wave solutions on FPU lattices
E. McMillian
1699 Dynamics of the convergence towards a self-similar blowup solution in a simplified model of aggregation
C. Huepe
1717 Dynamic stability of magnetic vortices
S. Gustafson

Source: Elizabeth Martin (

Table of Contents: Nonlinearity Volume 15(6), November 2002

All articles are free for 30 days after publication on the web.

Nonlinearity, 15(6), November 2002
1729 Some results for the line vortex equation
L.C. Berselli and H. Bessaih
1747 Soliton solutions for integrable equations in nonlinear optics: Bäcklund transformation approach
K. Nakkeeran
1755 The 2-link periodic orbits which maximise or minimise the length of a p-dimensional Birkhoff billiard are hyperbolic
M-C Arnaud
1759 Rigorous investigation of the Ikeda map by means of interval arithmetic
Z. Galias
1781 Conservation laws in cellular automata
M. Pivato
1795 Quadratic rational rotations of the torus and dual lattice maps
K.L. Kouptsov, J.H. Lowenstein and F. Vivaldi
1843 Axisymmetric capillary surfaces as a dynamical system
C.S. Riera and E. Risler
1881 Nevanlinna--Pick interpolation of attractors
C. Foias, M.S. Jolly and W-S Li
1905 Ruelle--Perron--Frobenius spectrum for Anosov maps
M. Blank, G. Keller and C. Liverani
1975 Remarks on 16th weak Hilbert problem for n=2
C. Li and Z. Zhang
1993 Classification of quadratic carrying simplices in two-dimensional competitive Lotka--Volterra systems
E.C. Zeeman
2019 An n-dimensional competitive Lotka--Volterra system is generically determined by the edges of its carrying simplex
E.C. Zeeman and M.L. Zeeman
2033 Trajectories in a neighbourhood of asymptotic surfaces of a priori unstable Hamiltonian systems
D. Treschev
2053 Billiards with positive topological entropy
C. Foltin
2077 Existence and stability of singular patterns in a Ginzburg--Landau equation coupled with a mean field
J. Norbury, J. Wei and M. Winter
2097 About a homoclinic pitchfork bifurcation in reversible systems with additional Z2-symmetry
T. Wagenknecht
2121 Noncoaxial multivortices in the complex sine-Gordon theory on the plane
I.V. Barashenkov, V.S. Shchesnovich and R.M. Adams
2147 Shear-thinning liquid films: macroscopic and asymptotic behaviour by quasi-self-similar solutions
L. Ansini and L. Giacomelli
2165 A scalar nonlocal bifurcation of solitary waves for coupled nonlinear Schrödinger equations
A.R. Champneys and J. Yang
2193 Remarks on the interaction between Born--Infeld solitons
Y. Brihaye and B. Hartmann
2201 AUTHOR INDEX (with titles), Volume 15

Source: Elizabeth Martin (

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Last Updated: 1 November 2002.