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: http://www.ams.org/notices/200001/fea-kopell.pdf.
Pages: 323--478
PAPERS
| 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 |
Pages: 479--972
PAPERS
| 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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