Хаотические колебания : вводный курс для научных работников и инженеров

This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field Emphasizing The Analysis Of Chaotic Vibrations In Physical And Experimental Systems, Chaotic Vibrations: An Introduction For Applied Scientists And Engineers Makes The New Mathematical Ideas In Nonlinear Dynamics And Chaos Understandable And Useful For Engineers And Scientists. It Gives Specific Examples And Applications Of Chaotic Dynamics And Is The Only Book To Explain How To Perform Both Computer And Physical Experiments In Chaotic Dynamics. Over 40 Exmaples Of Chaotic Systems Are Described. New Ideas In Dynamics Such As Poincaré Maps, Fractal Dimensions And Lyapunov Exponents Are Explained And Their Use Illustrated With Specific Examples. Coverage Includes Descriptions Of How To Recognize Chaotic Oscillations In Physical Experiments; Mathematical Models For Chaos And Physical Systems In Which Chaos Has Been Observed; Non-mathematical Descriptions Of Criteria For Chaos; And The Measurement Of Chaotic Dynamics. The Appendix Offers A Glossary Of Terms, Twelve Computer Experiments, And A Description Of Several Demonstration Experiments. An Extensive Guide To The Literature, Especially Work Relating To Physical Examples Of Chaotic Vibrations, With Over 200 References, It Is Included As Well. Engineers, Physicists, Mathematicians, And Others Will Find This Detailed Introduction A Valuable Guide To Understanding Chaotic Vibrations And Nonlinear Dynamics. -- From Dust Jacket. 1. Introduction: A New Age Of Dynamics -- What Is Chaotic Dynamics? -- Classical Nonlinear Vibration Theory: A Brief Review -- Maps And Flows -- 2. How To Identify Chaotic Vibrations -- 3. A Survey Of Systems With Chaotic Vibrations -- New Paradigms In Dynamics -- Mathematical Models Of Chaotic Physical Systems -- Physical Experiments In Chaotic Systems -- 4. Experimental Methods In Chaotic Vibrations -- Introduction: Experimental Goals -- Nonlinear Elements In Dynamical Systems -- Experimental Controls -- Phase Space Measurements -- Bifurcation Diagrams -- Experimental Poincaré Maps -- Quantitative Measures Of Chaotic Vibrations -- 5. Criteria For Chaotic Vibrations -- Introduction -- Empirical Criteria For Chaos -- Theoretical Predictive Criteria -- Lyapunov Exponents -- 6. Fractal Concepts In Nonlinear Dynamics -- Introduction -- Measures Of Fractal Dimension -- Fractal Dimension Of Strange Attractors -- Optical Measurement Of Fractal Dimension -- Fractal Basin Boundaries -- Complex Maps And The Mandelbrot Set. Francis C. Moon. A Wiley-interscience Publication. Includes Indexes. Bibliography: P. 287-299. Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. Topics cover Poincare maps, fractal dimensions and Lyapunov exponents, illustrating their use in specific physical examples. Includes an extensive guide to the literature, especially that relating to more mathematically oriented works; a glossary of chaotic dynamics terms; a list of computer experiments; and details for a demonstration experiment on chaotic vibrations. New mathematical ideas in nonlinear dynamics and chaos are translated in this book into a language that engineers and scientists can understand and specific examples and applications of chaotic dynamics in the physical world are given.