UK Nonlinear News, November 2003
ABSTRACT. Translation and rotation numbers have played an interesting and important role in the qualitative description of various dynamical systems. In this exposition we are especially interested in applications which lead to proofs of periodic motions in various kinds of dynamics on the annulus. The applications include billiards and geodesic flows.
Going beyond this simple qualitative invariant in the study of the dynamics of area preserving annulus maps, G.D. Birkhoff was led to the concept of ``regions of instability'' for twist maps. We discuss the closely related notion of instability sets for a generic area preserving surface diffeomorphism and develop their properties.
J. Franks. 2003. Rotation numbers and instability sets. Bulletin (New Series) of the American Mathematical Society, Volume 40, Number 3, pages 263-279.
The journal aims to publish in all areas of applications of dynamical systems to the sciences and engineering including bifurcation theory, differential equations, Hamiltonian and Lagrangian dynamics, ergodic theory and topological dynamics. High quality papers in all of these areas are welcome. The journal was given an impact factor of 1.300 in the ISI citation index for 2002.
We would especially encourage authors to consider submitting their papers to the journal in the following areas:
Papers for consideration should be sent to either of the following
editors:
Matthew Nicol, | Peter Ashwin |
Editorial Office, | Editorial Office |
Department of Mathematics and Statistics, | Department of Mathematical Sciences |
University of Surrey, | University of Exeter |
Guildford, GU2 7XH, | Exeter, EX4 4QE |
UK. | UK |
email: M.Nicol@surrey.ac.uk | dynsys@maths.ex.ac.uk |
Further information and details on submitting papers can be found at the instructions for authors webpage http://www.tandf.co.uk/journals/authors/cdssauth.asp.
Source: Matthew J. Nicol ( M.Nicol@surrey.ac.uk)
The Journal of Nonlinear Mathematical Physics will have two supplementary issues in 2003.
Supplement 1, Volume 10, September 2003:
"The Oeresund Symposium on Partial Differential Equations"
held in Lund (Sweden), May 23-25, 2002.
Editors: A. Constantin, G. Grubb, P.-A. Ivert, A. Melin and J.P. Solovej.
Currently in Press:
Supplement 2, Volume 10, December 2003:
Symmetries and Integrability of Difference Equations,
Proceedings of the EuroConference on Discrete Painlevé Equations and
the Solvability of Difference Equations
Editors: Yu. Suris et al
For orders or more information contact
Professor Norbert Euler
Managing Editor
Journal of Nonlinear Mathematical Physics
Department of Mathematics
Lulea University of Technology
SE-971 87 Lulea, Sweden
E-mail:
norbert@sm.luth.se
Fax +46 920-491073
http://www.sm.luth.se/math/JNMP/.
Source: Professor Norbert Euler
The September issue of the SMB Newsletter is on the web at http://www.smb.org/newsletter/.
It contains a report on ICIAM2003 and other items of interest to your readers.
Center: Raymond Mejía
Ciprian D. Coman | ||
pp. 1 - 22 | On a class of non-smooth oscillators | |
D. TurzÃk, M. DubcovÃ¡, A. KlÃ), P. Pokorny | ||
pp. 23 - 33 | Application of Bernoulli shift to investigation of stability of spatially periodic solutions in lattice dynamical systems | |
VÃtor AraÃºjo | ||
pp. 35 - 55 | Random perturbations of codimension one homoclinic tangencies in dimension 3 | |
J. A. Langa | ||
pp. 57 - 68 | Finite-dimensional limiting dynamics of random dynamical systems | |
Patrick Bonckaert, Vincent Naudot, Jiazhong Yang | ||
pp. 69 - 88 | Linearization of hyperbolic resonant germs | |
Ricardo Riaza, Pedro J. Zufiria | ||
pp. 89 - 105 | Differential-algebraic equations and singular perturbation methods in recurrent neural learning |
Source: Matthew J. Nicol ( M.Nicol@surrey.ac.uk)
Z. Bishnani, R. S. MacKay | |
pp. 107 - 129 | Safety criteria for aperiodically forced systems |
Peter Walters | |
pp. 131 - 138 | A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function |
Peter Ashwin, Gunter Ochs | |
pp. 139 - 158 | Convergence to local random attractors |
Florian Wagener | |
pp. 159 - 163 | A note on Gevrey regular KAM theory and the inverse approximation lemma |
Rafael R. Souza | |
pp. 165 - 179 | Sub-actions for weakly hyperbolic one-dimensional systems |
C. A. Morales | |
pp. 181 - 189 | Singular-hyperbolic sets and topological dimension |
Source: Matthew J. Nicol ( M.Nicol@surrey.ac.uk)
P. McSharry and P. Ruffino |
Asymptotic angular stability in non-linear systems: rotation numbers and winding numbers |
A. Shcherbina |
Gevrey regularity of the global attractor for the dissipative Zakharov system |
A. Halanay |
On the stability of some equilibrium points in a plankton population model |
X. Liao and K. Wong |
Convergence analysis of hybrid Bi-directional associative memory neural networks with discrete delays |
N. Sri Namachchivaya and H. van Rossel |
A centre manifold analysis of variable speed machining |
P. Walters |
Erratum |
Source: Matthew J. Nicol ( M.Nicol@surrey.ac.uk)
All articles are free for 30 days after publication on the web. http://stacks.iop.org/0951-7715/16/i=5
1565 M. Yampolsky | |
On the eigenvalues of a renormalization operator | |
1573 | H.E. Lomel\'{\i} and J.D. Meiss |
Heteroclinic intersections between invariant circles of volume-preserving maps | |
1597 | A. Yu Pogromsky, G. Santoboni and H. Nijmeijer |
An ultimate bound on the trajectories of the Lorenz system and its applications | |
1607 | A. Novikov |
Modulational stability of cellular flows | |
1641 | C.G.T. de Araujo Moreira and E.M. Mu\~noz Morales |
Sums of Cantor sets whose sum of dimensions is close to 1 | |
1649 | M. Rams |
Absolute continuity of the SBR measure for non-linear fat baker maps | |
1657 | L. Barreira |
Dimension estimates in nonconformal hyperbolic dynamics | |
1673 | C.M. Field and F.W. Nijhoff |
A note on modified Hamiltonians for numerical integrations admitting an exact invariant | |
1685 | S. Nonnenmacher |
Spectral properties of noisy classical and quantum propagators | |
1715 | P.B. Mucha |
On the inviscid limit of the Navier--Stokes equations for flows with large flux | |
1733 | B. Solomyak and H. Xu |
On the `Mandelbrot set' for a pair of linear maps and complex Bernoulli convolutions | |
1751 | H. Broer, H. Han{\ss}mann, \`A. Jorba, J. Villanueva and F. Wagener |
Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach | |
1793 | D.V. Zenkov and A.M. Bloch |
Invariant measures of nonholonomic flows with internal degrees of freedom | |
1809 | G. Fibich, B. Ilan and S. Schochet |
Critical exponents and collapse of nonlinear Schr\"odinger equations with anisotropic fourth-order dispersion | |
1823 | J.D. Gibbon, D.R. Moore and J.T. Stuart |
Exact, infinite energy, blow-up solutions of the three-dimensional Euler equations | |
1833 | G. Arioli and P. Zgliczy\'nski |
The H\'enon--Heiles Hamiltonian near the critical energy level---some rigorous results | |
1853 | X-S Yang and S. Zhang |
On the possibility of creating new asymptotically stable periodic orbits in continuous time dynamical systems by small feedback control | |
1861 | D.H. Kim and B.K. Seo |
The waiting time for irrational rotations | |
1869 | E. Herrera and R. Herrera |
A note on the relation between period and energy of periodic orbits near equilibrium points |
Source: Elizabeth Martin ( liz.martin@iop.org).
All articles are free for 30 days after publication on the web. http://stacks.iop.org/0951-7715/16/i=6
INVITED ARTICLE | |
R27 | P.J. Forrester |
Growth models, random matrices and Painlev\'e transcendents | |
PAPERS | |
1875 | A. Chertock, A. Kurganov and P. Rosenau |
Formation of discontinuities in flux-saturated degenerate parabolic equations | |
1899 | T. Kapela and P. Zgliczy\'nski |
The existence of simple choreographies for the N-body problem - a computer-assisted proof | |
1919 | P.J. Forrester and N.S. Witte |
Discrete Painlev\'e equations and random matrix averages | |
1945 | R. Dascaliuc |
On backward-time behaviour of Burgers' original model for turbulence | |
1967 | H. Bellout, S. Benachour and E.S. Titi |
Finite-time singularity versus global regularity for hyper-viscous Hamilton-Jacobi-like equations | |
1991 | B. Saussol and J. Wu |
Recurrence spectrum in smooth dynamical systems | |
2003 | K. Yagasaki |
Galoisian obstructions to integrability and Melnikov criteria for chaos in two-degree-of-freedom Hamiltonian systems with saddle centres | |
2013 | G. Verzini |
Bounded solutions to superlinear ODEs: a variational approach | |
2029 | T. Ozawa and Y. Yamazaki |
Life-span of smooth solutions to the complex Ginzburg--Landau type equation on a torus | |
2035 | E. Bogomolny and C. Schmit |
Asymptotic behaviour of multiple scattering on an infinite number of parallel half-planes | |
2061 | Y. Yang |
On Pokrovskii's anisotropic gap equations in superconductivity theory | |
2075 | P.V. Gordon |
An upper bound of the bulk burning rate in porous media combustion | |
2083 | P. Plech\'a\v c and V. \v Sver\'ak |
Singular and regular solutions of a nonlinear parabolic system | |
2099 | T.K. Callahan |
Hopf bifurcations on cubic lattices | |
2123 | M. Mourragui, E. Orlandi and E. Saada |
Macroscopic evolution of particle systems with random field Kac interactions | |
2149 | K.N. Webster and J.N. Elgin |
Asymptotic analysis of the Michelson system | |
2163 | D. Turaev and S. Zelik |
Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations | |
2199 | A. Fruchard and R. Schäfke |
Bifurcation delay and difference equations | |
2221 | |
AUTHOR INDEX (with titles), volume 16 |
Source: Elizabeth Martin ( liz.martin@iop.org).
All articles are free for 30 days after publication on the web. http://stacks.iop.org/0951-7715/17/i=1
COVER ILLUSTRATION | |
C1 | B. Krauskopf and H.M. Osinga |
The Lorenz manifold as a collection of geodesic level sets | |
PAPERS | |
1 | N. Simanyi |
Proving the ergodic hypothesis for billiards with disjoint cylindric scatterers | |
23 | R. Coutinho and B. Fernandez |
Fronts in extended systems of bistable maps coupled via convolutions | |
49 | J.S. C\'anovas |
Topological sequence entropy of interval maps | |
57 | J. Benoit, E. von Hauff and A. Saxena |
Self-dual bending theory for vesicles | |
67 | P.C. Moan |
On the KAM and Nekhoroshev theorems for symplectic integrators and implications for error growth | |
85 | J. Sieber and B. Krauskopf |
Bifurcation analysis of an inverted pendulum with delayed feedback control near a triple-zero eigenvalue singularity | |
105 | V. Afraimovich, A. Morante and E. Ugalde |
On the density of directional entropy in lattice dynamical systems | |
117 | R. Giamb\`o, F. Giannoni and P. Piccione |
Gravitational lensing in general relativity via bifurcation theory | |
133 | J. Su, J. Rubin and D. Terman |
Effects of noise on elliptic bursters | |
159 | H. Fuk\'s |
Probabilistic cellular automata with conserved quantities | |
175 | F. Abdenur, C. Bonatti and L.J. D\' \i az |
Non-wandering sets with non-empty interiors | |
193 | M. Kamenskii, O. Makarenkov and P. Nistri |
Small parameter perturbations of nonlinear periodic systems | |
207 | G. Friesecke and R.L. Pego |
Solitary waves on Fermi--Pasta--Ulam lattices: III. Howland-type Floquet theory | |
229 | G. Friesecke and R.L. Pego |
Solitary waves on Fermi--Pasta--Ulam lattices: IV. Proof of stability at low energy | |
253 | R.E. Beardmore, R. Laister and A. Peplow |
Trajectories of a DAE near a pseudo-equilibrium | |
281 | U. Kirchgraber and D. Stoffer |
Possible chaotic motion of comets in the Sun--Jupiter system---a computer-assisted approach based on shadowing | |
301 | S.C. Venkataramani |
Lower bounds for the energy in a crumpled elastic sheet---a minimal ridge | |
313 | J. Billingham |
Dynamics of a strongly nonlocal reaction--diffusion population model | |
347 | B. Rink |
A Cantor set of tori with monodromy near a focus--focus singularity | |
357 | J. Campos and M. Tarallo |
Large minimal period orbits of periodic autonomous systems |
Source: Elizabeth Martin ( liz.martin@iop.org).