High-Dimensional Chaotic and Attractor Systems

1. Front Matter

   Pages I-XV

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2. Introduction to Attractors and Chaos

   • Vladimir G. Ivancevic, Tijana T. Ivancevic

   Pages 1-151

3. Smale Horseshoes and Homoclinic Dynamics

   • Vladimir G. Ivancevic, Tijana T. Ivancevic

   Pages 153-222

4. 3–Body Problem and Chaos Control

   • Vladimir G. Ivancevic, Tijana T. Ivancevic

   Pages 223-284

5. Phase Transitions and Synergetics

   • Vladimir G. Ivancevic, Tijana T. Ivancevic

   Pages 285-418

6. Phase Synchronization in Chaotic Systems

   • Vladimir G. Ivancevic, Tijana T. Ivancevic

   Pages 419-455

7. Josephson Junctions and Quantum Engineering

   • Vladimir G. Ivancevic, Tijana T. Ivancevic

   Pages 457-489

8. Fractals and Fractional Dynamics

   • Vladimir G. Ivancevic, Tijana T. Ivancevic

   Pages 491-527

9. Turbulence

   • Vladimir G. Ivancevic, Tijana T. Ivancevic

   Pages 529-616

10. Geometry, Solitons and Chaos Field Theory

    • Vladimir G. Ivancevic, Tijana T. Ivancevic

    Pages 617-651

11. Back Matter

    Pages 653-702

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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.

• Soliton
• Transformation
• algorithm
• algorithms
• chaos
• chaos theory
• classification
• deterministic chaos
• mechanics
• model
• modeling
• molecular dynamics
• nonlinear dynamics
• stability

From the reviews:

"This is an ambitious book that … is devoted to the understanding, prediction and control of high-dimensional chaotic and attractor systems in real life. … Finally, and most usefully, the book has a substantial list of references (over 30 pages of them), meaning that the book can be used as a guide to literature in a diverse range of topics related to high- (and indeed low-) dimensional chaotic and nonlinear systems." (Peter Ashwin, Mathematical Reviews, Issue 2008 h)

• Defence Science and Technology Organisation, Adelaide, Australia

  Vladimir G. Ivancevic

• The University of Adelaide, Australia

  Tijana T. Ivancevic

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