UK Nonlinear News, November 2002.
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.
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 http://www.sciencearea.com.ua. For further details on this journal contact Arkadiy Tyshenko (info@tv-project.com.ua).
Source: Arkadiy Tyshenko (info@tv-project.com.ua).
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 (shh209f@smsu.edu)
All articles are free for 30 days after publication on the web. http://stacks.iop.org/0951-7715/15/i=5
Papers | |
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 ( liz.martin@iop.org).
All articles are free for 30 days after publication on the web. http://stacks.iop.org/0951-7715/15/i=6
Papers | |
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 Z_{2}-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 ( liz.martin@iop.org).