UK Nonlinear News, May 2000.


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Article: We Got Rhythm: Dynamical Systems of the Nervious System

Notices of the American Mathematical Society 47(1), January 2000, pages 6-16, contains an article by Nancy Kopell. This article, based on the 1999 Josiah Willard Gibbs lecture, discusses mathematical models for the rhythms that are observed in certain kinds of brain activity, as well as transitions between different rhythms. This article is avaiable as a pdf file at:

NONLINEARITY Contents list: Volume 13(2), March 2000

Pages: 323--478


323 G Gallavotti, G Gentile and V Mastropietro
  Hamilton--Jacobi equation, heteroclinic chains and Arnol'd diffusion in three time scale systems
341 A M F Rivas, M Saraceno and A M Ozorio de Almeida
  Quantization of multidimensional cat maps
377 F Takens and F O O Wagener
  Resonances in skew and reducible quasi-periodic Hopf bifurcations
397 A Celletti, A Giorgilli and U Locatelli
  Improved estimates on the existence of invariant tori for Hamiltonian systems
413 F Bernis, J Hulshof and J R King
  Dipoles and similarity solutions of the thin film equation in the half-line
441 J Etnyre and R Ghrist
  Contact topology and hydrodynamics: I. Beltrami fields and the Seifert conjecture
459 M Pudlak and V A Osipov
  Disclination vortices in elastic media
471 M J Ablowitz and S De Lillo
  On a Burgers--Stefan problem

NONLINEARITY Contents list: Volume 13(3), May 2000

Pages: 479--972


479 Z Zhou and L Feng
  A new estimate of the Hausdorff measure of the Sierpi\'nski gasket
493 C Fabry and J Mawhin
  Oscillations of a forced asymmetric oscillator at resonance
507 P D Miller, A Soffer and M I Weinstein
  Metastability of breather modes of time-dependent potentials
569 M J Grote and A J Majda
  Crude closure for flow with topography through large-scale statistical theory
601 M Bena\"{rm i} m
  Convergence with probability one of stochastic approximation algorithms whose
average is cooperative
617 V Afraimovich, A Maass and J Ur\'{rm i} as
  Symbolic dynamics for sticky sets in Hamiltonian systems
639 I Kukavica
  A ladder inequality for the Navier--Stokes equation
653 F Oliveira
  On the $C^{\infty}$ genericity of homoclinic orbits
663 W Sun
  Topological entropy and the complete invariant for expansive maps
675 K Promislow and J N Kutz
  Bifurcation and asymptotic stability in the large detuning limit of the
optical parametric oscillator
699 A Gasull, J Llibre, V Ma nosa and F Ma nosas
  The focus--centre problem for a type of degenerate system
731 A M\"unch
  Shock transitions in Marangoni gravity-driven thin-film flow
747 J P Keating and F Mezzadri
  Pseudo-symmetries of Anosov maps and spectral statistics
777 N Ju
  Estimates of asymptotic degrees of freedom for solutions to the Navier--Stokes equations
791 J W Bruce and F Tari
  Duality and implicit differential equations
813 J Qiao
  On the preimages of parabolic periodic points
819 P Ashwin, X-C Fu, T Nishikawa and K \.Zyczkowski
  Invariant sets for discontinuous parabolic area-preserving torus maps
837 A E Miroshnichenko, S V Dmitriev, A A Vasiliev and T Shigenari
  Inelastic three-soliton collisions in a weakly discrete sine-Gordon system
849 G Iooss
  Travelling waves in the Fermi--Pasta--Ulam lattice
867 G Gielis and R S MacKay
  Coupled map lattices with phase transition
889 M J Ablowitz, R Halburd and B Herbst
  On the extension of the Painlev\'e property to difference equations
907 R Wang and Z Zhang
  Exact stationary solutions of the Fokker--Planck equation for nonlinear oscillators under stochastic parametric and external excitations
921 E R Pujals and M Sambarino
  On homoclinic tangencies, hyperbolicity, creation of homoclinic orbits and variation of entropy
927 A Yu Pogromsky and H Nijmeijer
  On estimates of the Hausdorff dimension of invariant compact sets
947 E Bogomolny
  Action correlations in integrable systems

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Last updated: 3rd May 2000.