by H D I Abarbanel (UC, San Diego) , M I Rabinovich (UC, San Diego) , & M M Sushchik (UC, San Diego)

This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon.

• Introduction
• Nonlinear Oscillator without Dissipation
• Equilibrium States of a Nonlinear Oscillator with Dissipation
• Oscillations in Systems with Nonlinear Dissipation-Generators
• The Van der Pol Generator
• The Poincaré Map
• Slow and Fast Motions in Systems with One Degree of Freedom
• Forced Nonlinear Oscillators: Linear and Nonlinear Resonances
• Forced Generator: Synchronization
• Competition of Modes
• Poincaré Indices and Bifurcations of Equilibrium States
• Resonance Interactions between Oscillators
• Solitons
• Steady Propagation of Shock Waves
• Formation of Shock Waves
• Solitons. Shock Waves. Wave Interaction. The Spectral Approach
• Weak Turbulence. Random Phase Approximation
• Regular Patterns in Dissipative Media
• Deterministic Chaos. Qualitative Description
• Description of a Circuit with Chaos. Chaos in Maps
• Bifurcations of Periodic Motions. Period Doubling
• Controlled Nonlinear Oscillator. Intermittency
• Scenarios of the Onset of Chaos. Chaos through Quasi-Periodicity
• Characteristics of Chaos. Experimental Observation of Chaos
• Multidimensional Chaos. Discrete Ginzburg-Landau Model
• Problems to Accompany the Lectures