Table Of Content

List of contributors Ahlers, G. 421 Gollub, J.P. 501 Rom-Kedar, V. 248 Anderson, K.E. 444 Arecchi, F.T. 450 Hao, B.-l. 161 Savin, A.V. 316, 407 Holm, D. 177, 189 Scott, A.C. 333 Baxter,G.W. 465 Hiibler, A. 99 Segur, H. 109, 343 Behringer, R.P. 444, 465, 520 Shen, H. 555 Bivins, R.L. 3 lizuka, T. 388 Smale, S. 267 Bogoliubov, N.M. 43 Sreenivasan, K.R. 567 Brindley, J. 28 Jackson, E.A. 99 Stein, M.L. 3 Brucks, K.M. 39 Jauslin, H.R. 200 Steinberg, V. 596 Bullough, R. 43 Stribling, W.T. 531 Kaper, TJ. 205 Stylianou, 1. 316 Camassa, R. 295, 472 Kapitaniak, T. 28 Casdagli, M. 52 Kennedy, J. 213 Taylor, M.A. 274 Castillo, V.M. 539 Kevrekidis, 1.G. 274 Timonen, J. 43 Chang, K. 99 Kimura, Y. 512 Toh, S. 569 Chang, Y.-H. 109 Kodogeorgiou, A. 99 Tratnik, M.V. 308 Cocho, G. 119 Kovatic, G. 177, 226 Coppersmith, S.N. 131 Valkering, T.P. 360 Coutsias, E. 482 Lam, L. 539 Velgakis, MJ. 316 Cvitanovicé, P. 138 Louck, J.D. 23 Lynov, J.-P. 482 Wadati, M. 376, 388 David, D. 308 Waugh, F.R. 234 Deguchi, T. 376 Marcus, C.M. 234 Westervelt, R.M. 234 Diamond, B. 39 Martinez, D. 531 Wiggins, S. 205, 248, 472 Martinez-Mekler, G. 119 Wolf, K.B. 189 Ecke, R. 596 Matthaeus, W.H. 531 Wu, T.Y.-t. 295 El Naschie, M.S. 28 Metcalfe, G. 520 Epstein, LR. 152 Metropolis, N. 3 Xu, J.-J. 579 Eubank, S. 52 Montgomery, D. 531 Yajima, T. 388 Ohkitani, K. 569 Farmer, J.D. 52 Yamada, M. 569 Oughton, S. 531 Fisher, M.E. 498 Yorke, J.A. 213 Freimuth, R.D. 539 Pnevmatikos, S. 316, 407 Zeegers, Th. 360 Garcia, A. 539 Pochy, R.D. 539 Zhong, F. 596 Gibson, J. 52 Pomeau, Y. 546 Zolotaryuk, A.V. 316, 407 List of contributors Ahlers, G. 421 Gollub, J.P. 501 Rom-Kedar, V. 248 Anderson, K.E. 444 Arecchi, F.T. 450 Hao, B.-l. 161 Savin, A.V. 316, 407 Holm, D. 177, 189 Scott, A.C. 333 Baxter,G.W. 465 Hiibler, A. 99 Segur, H. 109, 343 Behringer, R.P. 444, 465, 520 Shen, H. 555 Bivins, R.L. 3 lizuka, T. 388 Smale, S. 267 Bogoliubov, N.M. 43 Sreenivasan, K.R. 567 Brindley, J. 28 Jackson, E.A. 99 Stein, M.L. 3 Brucks, K.M. 39 Jauslin, H.R. 200 Steinberg, V. 596 Bullough, R. 43 Stribling, W.T. 531 Kaper, TJ. 205 Stylianou, 1. 316 Camassa, R. 295, 472 Kapitaniak, T. 28 Casdagli, M. 52 Kennedy, J. 213 Taylor, M.A. 274 Castillo, V.M. 539 Kevrekidis, 1.G. 274 Timonen, J. 43 Chang, K. 99 Kimura, Y. 512 Toh, S. 569 Chang, Y.-H. 109 Kodogeorgiou, A. 99 Tratnik, M.V. 308 Cocho, G. 119 Kovatic, G. 177, 226 Coppersmith, S.N. 131 Valkering, T.P. 360 Coutsias, E. 482 Lam, L. 539 Velgakis, MJ. 316 Cvitanovicé, P. 138 Louck, J.D. 23 Lynov, J.-P. 482 Wadati, M. 376, 388 David, D. 308 Waugh, F.R. 234 Deguchi, T. 376 Marcus, C.M. 234 Westervelt, R.M. 234 Diamond, B. 39 Martinez, D. 531 Wiggins, S. 205, 248, 472 Martinez-Mekler, G. 119 Wolf, K.B. 189 Ecke, R. 596 Matthaeus, W.H. 531 Wu, T.Y.-t. 295 El Naschie, M.S. 28 Metcalfe, G. 520 Epstein, LR. 152 Metropolis, N. 3 Xu, J.-J. 579 Eubank, S. 52 Montgomery, D. 531 Yajima, T. 388 Ohkitani, K. 569 Farmer, J.D. 52 Yamada, M. 569 Oughton, S. 531 Fisher, M.E. 498 Yorke, J.A. 213 Freimuth, R.D. 539 Pnevmatikos, S. 316, 407 Zeegers, Th. 360 Garcia, A. 539 Pochy, R.D. 539 Zhong, F. 596 Gibson, J. 52 Pomeau, Y. 546 Zolotaryuk, A.V. 316, 407 Analytic subject index alpha-helix 333 dielectric breakdown model 539 amplitude equations 501 diffusion, Arnold 177 anisotropy 579 diffusion, nonlinear 555 annealing 234 domain walls 498 anyon theory 43 dry hydrodynamics 450 associative memory 234 dynamical systems 213, 267 asymptotic 109, 579 auto-expansions 39 electrodeposit 539 automata 465 embedding 52 enstrophy 569 basin of attraction 213 Ewald lattice 531 bifurcations 421 exponentially small 109 boson coherent state 555 extinction 274 boundary conditions, no-slip 482 boundary-layer interactions 482 Faraday instability 501 Braid group 376 fluctuations 421 fractal 539 cellular automata 465 Fredholm determinants 138 chaos 52, 161, 200, 267 chaos, adiabatic 205 general resonance 99 chaotic advection 248 genetic evolution 119 charge density waves 131 geometrical optics 177 chemical oscillations 152, 274 global mode 579 coherent vortices 482, 531 grammatical complexity 161 collapse 512 granular flow 465 commensurate phases 498 competition 520 Hamiltonian systems 226, 472 complex-time singularity 512 Hénon map symbolic dynamics 138 computational fluid dynamics 482 homoclinic chaos 177 continuation 274 homoclinic orbits 189, 248 convection 520 homotopy method 226 convection, binary mixture 444 Hopf bifurcation 28 coupled map lattices 119 hydrogen-bonded chains 407 coupled oscillators 274 crustacean stomatogastric ganglion 152 instability, nonlinear 596 integrability 43, 343 Davydov 333 integrable, completely 343 defect nucleation 546 interfaces 498 delay-differential equations 234 dendrite growth 579 kink dynamics 407 deterministic chaotic systems 138 kneading theory 39, 161 610 Analytic subject index knot theory 376 random process 52, 539 Korteweg—de Vries equation, forced 295 random vortex method 555 ray tracing 189 Lie—Poisson dynamics 189 ray trapping 177, 189 lifetime 333 Rayleigh-Bénard convection 444 link polynomial 376 reaction—diffusion processes 119 lobe area 205, 226 resonance 274 lobes dynamics 248 ribosome 119 localized states 421, 444 rotation 596 map of the intervals 3 scaling law 512 Markov model 248 Schrédinger equation, unstable nonlinear 388 Melnikov function 109 selective decay 531 Melnikov function, adiabatic 205 separatrix 248 mesoscopic 200 shear flow 567, 569 modeling 99 solitary waves 295 soliton 308, 316, 333, 343, 360, 388, 407 neural networks 234 solvable models, exactly 376 neural oscillators 152 space-time complexity 450 noise amplification 52 spatio-temporal 520 nonconservative dynamics 555 spatio-temporal chaos 501 nongradient flows 546 spatio-temporal intermittency 546 nonlinear optics 450 spectral methods 482 nonlinear physics 316 spectroscopy 99 nonlinear transfer 555 stability 295 State space 52 one-dimensional chain 360 Statistical mechanics, quantum and classical 43 optical fiber 308 stochastic effects 421 oscillation 234 strange attractor 28 structure 343 parabolic map 3 superfluid 520 parametrically forced pendulum 205 symbolic dynamics 161 passive tracer 472 symmetry 109 pattern competition 444 pattern formation 152, 539 Temperley—Lieb algebra 376 pendulum 109 thermal convection 596 period doubling 360 time dependent convection 472 periodic orbit expansions 138 time series 52 phase diagrams 498 topological entropy 39, 161 phase organization 131 transport 226, 248, 472, 501 phase slips 131 traveling waves, nonlinear 444 polarization 308 travelling waves 421 prediction 52 turbulence 520, 531, 546, 567, 569 problems 267 Turing structures 152 protein 333 turnstile 248 protonic conductivity 316 universality 567 quantum scattering 200 unstable media 388 Analytic subject index van der Pol’s oscillator 28 Yang-—Baxter relation 376 variational theory 205 vortex motion 512 Wada property 213 Zener tunneling 200 wavenumber selection 421 zeta functions 138 waves 501