Universality in chaos : a reprint selection

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Bibliographic Information

Universality in chaos : a reprint selection

compiled and introduced by Predrag Cvitanović

Adam Hilger, 1989

2nd ed

  • : pbk

Available at  / 54 libraries

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Includes bibliographical references and index

Description and Table of Contents

Volume

ISBN 9780852742594

Description

This book presents developments in the study of the chaotic behaviour of deterministic systems. It concentrates on the universal aspects of chaotic motions: those qualitative and quantitative predictions which apply to large classes of physical systems. The selection can be divided into roughly four parts. The first part offers a general introduction to deterministic chaos and universality. The second part presents some of the experimental evidence for universality in transitions to turbulence. The third part concentrates on the theoretical investigations of the universality of ideas, and the last part gives a glimpse of the further developments stimulated by the success of the one-dimensional universality theory.

Table of Contents

  • Part 1: strange attractors, D.Ruelle
  • universal behaviour in nonlinear systems, M.J.Feignbaum
  • simple mathematical models with very complicated dynamics, R.M.May
  • roads to turbulence in dissapative dynamical systems, J.P.Eckmann. Part 2 Experiments: a Rayleigh Benard experiment - helium in a small box, A.Libchaber and J.Mauer
  • period doubling cascade in mercury, a quantitative measurement, A.Libchaber et al
  • onset of turbulence in a rotating fluid, J.P.Gollub and H.L.Swinney
  • transition to chaotic behaviour via a reproducible sequence of period-doubling bifurcations, M.Giglio et al
  • intermittency in Rayleigh-Bernard convection, P.Berge et al
  • representation of a strange attractor from an experimental study of chemical turbulence, J.C.Roux et al
  • chaos in the Belousov-Zhabotinskii reaction, J.L.Hudson and J.C.Mankin
  • one-dimensional dynamics in a multicomponent chemical reaction, R.H.Simoyi et al
  • experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser, F.T.Arrechi et al
  • evidence for universal chaotic behaviour of a driven nonlinear oscillator, J.Testa et al
  • phase locking, period boubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells, M.R.Guevara et al. Part 3 Theory: on finite limits sets for transformations on the unit interval, M.Metropolis et al
  • the universal metric properties of nonlinear transformations, M.J.Feigenbaum
  • a computer-assisted proof of the Feigenbaum conjectures, O.E.Lanford
  • the transition to aperiodic behaviour in turbulent systems, M.J.Feigenbaum
  • universality and the power spectrum at the onset of chaos, M.Nauenberg and J.Rudnick. Part 4 Noise: invariant distributions and stationary correlation functions of one dimensional discrete processes, S.Grossmann and S.Thomae
  • noise periodicity and reverse bifurcation, E.N.Lorenz
  • scaling behaviour of chaotic flows, B.A.Huberman and J.Rudnick
  • universal and power spectra for the reverse bifurcation sequence, A.Wolf and J.Swift
  • power spectra of strange attractors, B.A.Huberman and A.B.Zisook
  • spectral broadening of period-doubling bifurcation sequences, J.D.Farmer
  • fluctuations and the onset of chaos, J.P.Crutchfield and B.A.Huberman
  • scaling theory for noisy period-doubling transitions to chaos, B.Shraiman et al
  • scaling for external noise at the onset of chaos. Part 5 Intermittency. Part 6 Period-doubling in higher dimensions. Part 7 Beyond the one-dimensional theory. Part 8 Recent developments. (Part contents)
Volume

: pbk ISBN 9780852742600

Description

Nature provides many examples of physical systems that are described by deterministic equations of motion, but that nevertheless exhibit nonpredictable behavior. The detailed description of turbulent motions remains perhaps the outstanding unsolved problem of classical physics. In recent years, however, a new theory has been formulated that succeeds in making quantitative predictions describing certain transitions to turbulence. Its significance lies in its possible application to large classes (often very dissimilar) of nonlinear systems. Since the publication of Universality in Chaos in 1984, progress has continued to be made in our understanding of nonlinear dynamical systems and chaos. This second edition extends the collection of articles to cover recent developments in the field, including the use of statistical mechanics techniques in the study of strange sets arising in dynamics. It concentrates on the universal aspects of chaotic motions, the qualitative and quantitative predictions that apply to large classes of physical systems. Much like the previous edition, this book will be an indispensable reference for researchers and graduate students interested in chaotic dynamics in the physical, biological, and mathematical sciences as well as engineering.

Table of Contents

Introductory articles: Strange attractors. Universal behaviour in nonlinear systems. Simple mathematical models with very complicated dynamics. Experiments: Onset of turbulence in a rotating fluid Transition to chaotic behaviour via a reproducible sequence of period-doubling bifurcations. Representation of a strange attractor fron an experimental study of chemical turbulence. One-dimensional dynamics in a multicomponent chemical reaction. Experimental evidence of subharmonic bifurcations, multistability and turbulence in a Q-switched gas laser. Evidence for universal chaotic behaviour of a driven nonlinear oscillator. Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Theory: Qualitative universality in one dimension. Quantitative universality for one-dimensional period-doublings. A computer-assisted proof of the Feigenbaum conjectures. The transition to aperiodic behaviour in turbulent systems. Noise: Deterministic noise. Invariant distributions and stationary correlation functions of one-dimensional discrete processes. Scaling behaviour of chaotic flows. Power spectra of strange attractors. External noise: Fluctuations and the onset of chaos. Scaling for external noise at the onset of chaos. Intermittency: Intermittent transition to turbulence in dissipative dynamical system. Period-doubling in higher dimensions: A two-dimensional mapping with a strange attractor. Period doubling bifurcations for families of maps on R. Sequences of infinite bifurcations and turbulence in a five-mode truncation of the Navier-Stokes equations. Beyond the one-dimensional theory: Scaling behaviour in a map of a circle onto itself: empirical results. Self-generated chaotic behaviour in nonlinear mechanics. Recent developments: Feigenbaum universality and the thermodynamic formalism. Fractal measures and their singularities: the characterization of strange sets. Fixed points of composition operators.

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