# Universality in Chaos, 2nd edition

DOI link for Universality in Chaos, 2nd edition

Universality in Chaos, 2nd edition book

# Universality in Chaos, 2nd edition

DOI link for Universality in Chaos, 2nd edition

Universality in Chaos, 2nd edition book

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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

part |2 pages

Introduction

part 1|2 pages

Introductory Articles

part 2|2 pages

Experiments

chapter |6 pages

#### Period doubling cascade in mercury, a quantitative measurement

chapter |3 pages

#### Transition to Chaotic Behavior via a Reproducible Sequence of Period-Doubling Bifurcations

chapter |4 pages

#### Intermittency in Rayleigh-Bénard convection

chapter |3 pages

#### Representation of a Strange Attractor from an Experimental Study of Chemical Turbulence

chapter |3 pages

#### One-Dimensional Dynamics in a Multicomponent Chemical Reaction

chapter |4 pages

#### Intermittent behaviour in the Belousov-Zhabotinsky reaction

chapter |4 pages

#### Experimental Evidence of Subharmonic Bifurcations, Multistabilìty, and Turbulence in a Q-Switched Gas Laser

chapter |4 pages

#### Evidence for Universal Chaotic Behavior of a Driven Nonlinear Oscillator

chapter |7 pages

#### Phase Locking, Period-Doubling Bifurcations, and Irregular Dynamics in Periodically Stimulated Cardiac Cells

part 3|2 pages

Theory

chapter 17|22 pages

#### On Finite Limit Sets for Transformations on the Unit Interval

chapter |38 pages

#### The Universal Metric Properties of Nonlinear Transformations

chapter |22 pages

#### The Transition to Aperiodic Behavior in Turbulent Systems

chapter |3 pages

#### Universality and the power spectrum at the onset of chaos

part 4|2 pages

Noise

chapter |11 pages

#### Invariant Distributions and Stationary Correlation Functions of One-Dimensional Discrete Processes

chapter |3 pages

#### Universal Power Spectra for the Reverse Bifurcation Sequence

chapter |4 pages

#### Scaling Theory for Noisy Period-Doubling Transitions to Chaos

chapter |4 pages

#### Scaling for External Noise at the Onset of Chaos

part 5|2 pages

Intermittency

chapter |9 pages

#### Intermittent Transition to Turbulence in Dissipative Dynamical Systems

chapter 32|3 pages

#### Intermittency in the Presence of Noise: A Renormalization Group Formulation

part 6|2 pages

Period-doubling in Higher Dimensions

chapter |14 pages

#### Period Doubling Bifurcations for Families of Maps on ℝn

chapter |20 pages

#### Sequences of Infinite Bifurcations and Turbulence in a Five-Mode Truncation of the Navier–Stokes Equations

chapter |4 pages

#### Power Spectral Analysis of a Dynamical System*

part 7|2 pages

Beyond the One-dimensional Theory

chapter |7 pages

#### Scaling Behavior in a Map of a Circle Onto Itself: Empirical Results*

chapter 41|69 pages

#### Self-Generated Chaotic Behavior in Nonlinear Mechanics §

part 8|2 pages

Recent Developments