© 2010

Hamiltonian Chaos Beyond the KAM Theory

Dedicated to George M. Zaslavsky (1935–2008)

  • Albert C. J. Luo
  • Valentin Afraimovich


  • Explains a theory on resonant mechanism of Hamiltonian chaos in stochastic layers and webs

  • Develops newest methods and ideas on Hamiltonian chaos in nonlinear Hamiltonian systems

  • Direct applies Hamiltonian chaos to quantum dynamics and ray dynamics

  • Predicts Hamiltonian chaos beyond the KAM theory


Part of the Nonlinear Physical Science book series (NPS, volume 0)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. S. M. Soskin, R. Mannella, O. M. Yevtushenko, I. A. Khovanov, P. V. E. McClintock
    Pages 51-141
  3. T. M. Fromhold, A. A. Krokhin, S. Bujkiewicz, P. B. Wilkinson, D. Fowler, A. Patanè et al.
    Pages 225-254
  4. A. L. Virovlyansky
    Pages 255-296
  5. Back Matter
    Pages 297-297

About this book


“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.


Dynamical systems George Zaslavsky HEP Hamiltonian chaos KAM Theory NPS Nonlinear Hamiltonian systems Quantum chaos Resonant layers Stochastic layers and Webs chaos nonlinear dynamics

Editors and affiliations

  • Albert C. J. Luo
    • 1
  • Valentin Afraimovich
    • 2
  1. 1.Department of Mechanical and Industrial EngineeringSouthern Illinois University EdwardsvilleEdwardsvilleUSA
  2. 2.IICO-UASLPSan Luis Potosi SLPMexico

Bibliographic information