Instabilities in Dynamical Systems - Applications to Celestial Mechanics (Paperback, Softcover reprint of the original 1st ed. 1979)

ix List of Speakers and Participants xi Group Photograph xviii Greetings by B. Garfinkel, A. E. Roy and P. J. Message xix Introduction xxiii PART I: FUNDAMENTAL CONSIDERATIONS OF STABILITY R. BROUCKE/Simple Non-Integrable Systems with Two Degrees of Freedom 3 G. CONTOPOULOS/lnstabilities in Systems of Three Degrees of Freedom 25 R. W. EASTON/Perturbed Twist Maps, Homoclinic Points and Ergodic Zones 41 O. GUREL/Bifurcation Theory and its Applications V. SZEBEHELY/General Considerations of Stability in 49 61 Celestial Mechanics PART II: ASPECTS OF NUMERICAL ANALYSIS AND STATISTICAL MECHANICS S. J. AARSETH/An N-Body Integration Method in Co-Moving Coordinates 69 J. BAUMGARTE/The General Theory of Conservative Stabilization of the Keplerian Problem 81 C. DEWITT-MORETTE /Celestial Mechanics, Quantum Mechanics, and Path Integration 95 G. C. STEY/Statistical Viewpoint in Classical Mechanics 103 PART III: STABILITY OF PLANETARY SYSTEMS ~ C. FROESCHLE and H. SCHOLL/Evolution of Orbits in the Outer Part of the Asteroidal Belt and in the Kirkwood Gaps as Influenced by the Mass Effects of Saturn and Jupiter 115 v TABLE OF CONTENTS vi B. GARFINKEL/On the Stability of Resonant Motion in 121 the Light of the Regularizing Function 129 P. GOLDREICH/The Rings of Saturn and Uranus J. D. HADJIDEMETRIOU/Instabilities in Periodic 135 Planetary-Type Orbits P. J. MESSAGE/Bounds on Secular Terms in Celestial 165 Mechanics A. E. ROY/Empirical Stability Criteria in the 177 Many-Body Problem R. O. VICENTE/Instabilities in Planetary Systems 211 PART IV: THE PROBLEM OF THREE BODIES H.