UK Nonlinear News, August 1999.


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Article: Developments in Chaotic Dynamics

Lai-Sang Young has written a review aimed at a general mathematics community of some of the developments since the 1960s in the subject of hyperbolic dynamics, using billiards and Hénon attractors as illustrative examples.

"This article is about nonuniformly hyperbolic systems, with emphasis on their ergodic theory. I would like to focus on the following two directions of progress: the development of a general theory and the applications of hyperbolic techniques to specific examples. I will select two sample results from each one of these directions and discuss some of the ideas behind the theorems. The two applications that I have chosen are billiards and Hénon attractors. For the general theory part, my two topics are (1) Lyapunov exponents, entropy, and dimension; and (2) correlation decay and central limit theorem."

Notices of the American Mathematical Society, 45, Number 10, November 1988, pages 1318-1328.

New issue of Dynamic Notes

The SIAM Activity Group on Dynamical Systems has released Dynamics Notes Volume 1999.01. The issue has not yet appeared on the Group's infrequently used Web Pages.

NONLINEARITY Contents list: Volume 12(4), July 1999

741P. Ashwin, I. Melbourne and M. Nicol
Drift bifurcations of relative equilibria and transitions of spiral waves
757 G.E. Roberts
Spectral instability of relative equilibria in the planar n-body problem
771 C.E. Elmer and E.S. Van Vleck
Analysis and computation of travelling wave solutions of bistable differential-difference equations
799 K. Yagasaki
The method of Melnikov for perturbations of multi-degree-of-freedom Hamiltonian systems
823 D. Bambusi
On long time stability in Hamiltonian perturbations of non-resonant linear PDEs
851 N.S. Manton and S.M. Nasir
Conservation laws in a first-order dynamical system of vortices
867 Y. Brihaye and T.N. Tomaras
The Goldstone model static solutions on S1
877 K.J. Falconer
Generalized dimensions of measures on self-affine sets
893 J.C. Martín
Hopf bifurcations and homoclinic tangencies
903 R. Martínez and C. Simó
Simultaneous binary collisions in the planar four-body problem
931 R. Halburd
Integrable relativistic models and the generalized Chazy equation
939 P. Cvitanovi\'c, C.P. Dettmann, R. Mainieri and G. Vattay
Trace formulae for stochastic evolution operators: smooth conjugation = method
955 P.R. Gordoa, N. Joshi and A. Pickering
Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations
969 S. Slijep\v{c}evi\'{c}
Monotone gradient dynamics and Mather's shadowing
987 M.A. Singer and P.M. Sutcliffe
Symmetric instantons and Skyrme fields
1005 P.J. Rippon and G.M. Stallard
Families of Baker domains: I
1013 M. Blinov and Y. Yomdin
Generalized centre conditions and multiplicities for polynomial Abel equations of small degrees
1029 G. Froyland
Ulam's method for random interval maps
1053 E.J. Beggs and P.R. Johnson
Loop groups and the symplectic form for solitons in integrable theories
1071 M.P. Brenner, P. Constantin, L.P. Kadanoff, A. Schenkel and S.C. Venkataramani
Diffusion, attraction and collapse
1099 C. Christopher and S. Lynch
Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
1113 T. Harayama, A. Shudo and S. Tasaki
Semiclassical Fredholm determinant for strongly chaotic billiards
1151 Yi Wang, Ling Yang and Huimin Xie
Complexity of unimodal maps with aperiodic kneading sequences
1177 A. Algaba, E. Freire, E. Gamero and A.J. Rodríguez-Luis
A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation
1207 G. Yuan and B.R. Hunt
Optimal orbits of hyperbolic systems
1225 P. Collet, A. Galves and B. Schmitt
Repetition times for Gibbsian sources

Source: Elizabeth Martin (

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