Instabilities in Dynamical Systems: Applications to Celestial Mechanics

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.