Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935—2008)

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Albert C. J. Luo, Valentin Afraimovich
Springer Science & Business Media, Jan 4, 2011 - Science - 292 pages

“Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935—2008)” covers the recent developments and advances in the theory and application of Hamiltonian chaos in nonlinear Hamiltonian systems. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. Each chapter in this book was written by well-established scientists in the field of nonlinear Hamiltonian systems. The development presented in this book goes beyond the KAM theory, and the onset and disappearance of chaos in the stochastic and resonant layers of nonlinear Hamiltonian systems are predicted analytically, instead of qualitatively. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.

 

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Contents

Chapter 1 Stochastic and Resonant Layers in Nonlinear Hamiltonian Systems
1
Chapter 2 A New Approach to the Treatment of Separatrix Chaos and Its Applications
51
Chapter 3 Hamiltonian Chaos and Anomalous Transport in Two Dimensional Flows
143
Chapter 4 Hamiltonian Chaos with a Cold Atom in an Optical Lattice
193
Chapter 5 Using Stochastic Webs to Control the Quantum Transport of Electrons in Semiconductor Superlattices
224
Chapter 6 Chaos in Ocean Acoustic Waveguide
255
Nonlinear PhysicarScience
297
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