Ebook: High-Dimensional Chaotic and Attractor Systems: A Comprehensive Introduction

If we try to describe real world in mathematical terms, we will see that real life is very often a high–dimensional chaos. Sometimes, by ‘pushing hard’, we manage to make order out of it; yet sometimes, we need simply to accept our life as it is. To be able to still live successfully, we need tounderstand, predict, and ultimately control this high–dimensional chaotic dynamics of life. This is the main theme of the present book. In our previous book, Geometrical - namics of Complex Systems, Vol. 31 in Springer book series Microprocessor– Based and Intelligent Systems Engineering, we developed the most powerful mathematical machinery to deal with high–dimensional nonlinear dynamics. In the present text, we consider the extreme cases of nonlinear dynamics, the high–dimensional chaotic and other attractor systems. Although they might look as examples of complete disorder – they still represent control systems, with their inputs, outputs, states, feedbacks, and stability. Today, we can see a number of nice books devoted to nonlinear dyn- ics and chaos theory (see our reference list). However, all these books are only undergraduate, introductory texts, that are concerned exclusively with oversimpli?ed low–dimensional chaos, thus providing only an inspiration for the readers to actually throw themselves into the real–life chaotic dynamics.

This is a graduate–level monographic textbook devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective of the book is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics.

From introductory material on the low-dimensional attractors and chaos, the text moves on to explore Smale’s topological transformations of stretching, squeezing and folding; Poincar?’s 3-body problem and basic techniques of chaos control; phase synchronization in high-dimensional chaotic systems. Additional topics include high-tech Josephson junctions, the basic components for the future quantum computers; fractals and fractional Hamiltonian dynamics; a review of modern techniques for dealing with turbulence, ranging from the parameter–space of the Lorenz attractor to the Lie symmetries. The concluding chapter offers a brief on the cutting edge techniques of the high-dimensional nonlinear dynamics (including geometries, gauges and solitons, culminating into the chaos fi

This is a graduate–level monographic textbook devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective of the book is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics.

From introductory material on the low-dimensional attractors and chaos, the text moves on to explore Smale’s topological transformations of stretching, squeezing and folding; Poincar?’s 3-body problem and basic techniques of chaos control; phase synchronization in high-dimensional chaotic systems. Additional topics include high-tech Josephson junctions, the basic components for the future quantum computers; fractals and fractional Hamiltonian dynamics; a review of modern techniques for dealing with turbulence, ranging from the parameter–space of the Lorenz attractor to the Lie symmetries. The concluding chapter offers a brief on the cutting edge techniques of the high-dimensional nonlinear dynamics (including geometries, gauges and solitons, culminating into the chaos fi
Content:
Front Matter....Pages I-XV
Introduction to Attractors and Chaos....Pages 1-151
Smale Horseshoes and Homoclinic Dynamics....Pages 153-222
3–Body Problem and Chaos Control....Pages 223-284
Phase Transitions and Synergetics....Pages 285-418
Phase Synchronization in Chaotic Systems....Pages 419-455
Josephson Junctions and Quantum Engineering....Pages 457-489
Fractals and Fractional Dynamics....Pages 491-527
Turbulence....Pages 529-616
Geometry, Solitons and Chaos Field Theory....Pages 617-651
Back Matter....Pages 653-702

This is a graduate–level monographic textbook devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective of the book is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics.

From introductory material on the low-dimensional attractors and chaos, the text moves on to explore Smale’s topological transformations of stretching, squeezing and folding; Poincar?’s 3-body problem and basic techniques of chaos control; phase synchronization in high-dimensional chaotic systems. Additional topics include high-tech Josephson junctions, the basic components for the future quantum computers; fractals and fractional Hamiltonian dynamics; a review of modern techniques for dealing with turbulence, ranging from the parameter–space of the Lorenz attractor to the Lie symmetries. The concluding chapter offers a brief on the cutting edge techniques of the high-dimensional nonlinear dynamics (including geometries, gauges and solitons, culminating into the chaos fi
Content:
Front Matter....Pages I-XV
Introduction to Attractors and Chaos....Pages 1-151
Smale Horseshoes and Homoclinic Dynamics....Pages 153-222
3–Body Problem and Chaos Control....Pages 223-284
Phase Transitions and Synergetics....Pages 285-418
Phase Synchronization in Chaotic Systems....Pages 419-455
Josephson Junctions and Quantum Engineering....Pages 457-489
Fractals and Fractional Dynamics....Pages 491-527
Turbulence....Pages 529-616
Geometry, Solitons and Chaos Field Theory....Pages 617-651
Back Matter....Pages 653-702
....