Contents Preface Vii Contents Vii Chapter 1. Deterministic chaos and nonlinear dynamics Classification of all cycles of the parabolic map R.L. Bivins, J.D. Louck, N. Metropolis and M.L. Stein 3 Analytical conditions for strange chaotic and nonchaotic attractors of the quasiperiodically forced van der Pol equation J. Brindley, T. Kapitaniak and M.S. El Naschie 28 Monotonicity of auto-expansions K.M. Brucks and B. Diamond 39 Quantum and classical integrability: new approaches in statistical mechanics R. Bullough, N.M. Bogoliubov and J. Timonen 43 State-space reconstruction in the presence of noise M. Casdagli, S. Eubank, J.D. Farmer and J. Gibson 52 General resonance spectroscopy K. Chang, A. Kodogeorgiou, A. Hiibler and E.A. Jackson 99 An asyptotic symmetry of the rapidly forced pendulum Y.-H. Chang and H. Segur 109 On a coupled map lattice formulation of the evolution of genetic sequences G. Cocho and G. Martinez-Mekler 119 Nonlinear dynamics of sliding charge density waves S.N. Coppersmith 13] Periodic orbits as the skeleton of classical and quantum chaos P. Cvitanovic 138 Nonlinear oscillations in chemical and biological systems I.R. Epstein 152 Symbolic dynamics and characterization of complexity B.-1. Hao 161 Homoclinic chaos for ray optics in a fiber D. Holm and G. Kovaéié 177 Lie—Poisson description of Hamiltonian ray optics D. Holm and K.B. Wolf 189 Chaotic properties in quantum scattering H.R. Jauslin 200 Lobe area in adiabatic Hamiltonian systems T.J. Kaper and S. Wiggins 205 Basins of Wada J. Kennedy and J.A. Yorke Lobe area via action formalism in a class of Hamiltonian systems G. Kovacicé Nonlinear dynamics and stability of analog neural networks C.M. Marcus, F.R. Waugh and R.M. Westervelt 234 Transport in two-dimensional maps: Concepts, examples and a comparison of the theory of Rom-Kedar and Wiggins with the Markov model of Meiss, Ott and Percival V. Rom-Kedar and S. Wiggins 248 Dynamics retrospective: Great problems, attempts that failed S. Smale 267 Some common dynamic features of coupled reacting systems M.A. Taylor and I.G. Kevrekidis 274 Chapter 2. Solitons and coherent structures Stability of some stationary solutions for the forced KdV equation R. Camassa and T.Y.-t. Wu 295 Polarization modulated solitary waves in an optical fiber D. David and M.V. Tratnik 308 Proton transport by solitons S. Pnevmatikos, A.V. Savin, I. Stylianou, M.J. Velgakis and A.V. Zolotaryuk 316 Davydov’s soliton revisited A.C. Scott 333 Who cares about integrability? H. Segur 343 Period doubling solitons: yes or no? T.P. Valkering and Th. Zeegers 360 Old and new link polynomials from the theory of exactly solvable models M. Wadati and T. Deguchi 376 Soliton phenomena in unstable media M. Wadati, T. lizuka and T. Yajima 388 Two-sublattice kink dynamics and ionic defects in hydrogen-bonded chains A.V. Zolotaryuk, S. Pnevmatikos and A.V. Savin Chapter 3. Patterns and turbulence Experiments with pattern-forming systems G. Ahlers Traveling wave convection patterns in an annular cell K.E. Anderson and R.P. Behringer Space-time complexity in nonlinear optics F.T. Arecchi Cellular automata models for the flow of granular materials G.W. Baxter and R.P. Behringer Transport of a passive tracer in time-dependent Rayleigh—Bénard convection R. Camassa and S. Wiggins 472 Fundamental interactions of vortical structures with boundary layers in two-dimensional flows E. Coutsias and J.-P. Lynov 482 Interfaces, membranes: rough, smooth and interacting M.E. Fisher 498 Nonlinear waves: dynamics and transport J.P. Gollub 501 Vortex collapse from a viewpoint of complex-time singularity Y. Kimura 512 Using superfluid mixtures to probe convective instabilities G. Metcalfe and R.P. -Behringer 520 Decaying, two-dimensional, Navier-Stokes turbulence at very long times W.H. Matthaeus, W.T. Stribling, D. Martinez, S. Oughton and D. Montgomery 53] Electrodeposit tree patterns in linear cells: Experiment and computer models R.D. Pochy, A. Garcia, R.D. Freimuth, V.M. Castillo and L. Lam 539 Extended systems: the impact of nonlinear science Y. Pomeau 546 Nonconservative dynamics of vortical structures: A statistical-mechanical perspective H. Shen 555 Do scalar fluctuations in turbulent shear flows possess local universality? K.R. Sreenivasan 567 Enstrophy and momentum fluxes in two-dimensional shear flow turbulence S. Toh, K. Ohkitani and M. Yamada 569 Two-dimensional dendritic growth with anisotropy of surface tension J.-J. Xu 579 Rotating Rayleigh—Bénard convection: Kiippers—Lortz transition F. Zhong, R. Ecke and V. Steinberg 596 List of contributors 608 Analytic subject index