Periodic Orbits, Stability and Resonances, Softcover reprint of the original 1st ed. 1970
Proceedings of a Symposium Conducted by the University of São Paulo, the Technical Institute of Aeronautics of São José Dos Campos, and the National Observatory of Rio De Janeiro, at the University of São Paulo, São Paulo, Brasil, 4-12 September, 1969

The subjects of resonance and stability are closely related to the problem of evolution of the solar system. It is a physically involving problem and the methods available to mathematics today seem unsatisfactory to produce pure non linear ways of attack. The linearization process in both subjects is clearly of doubtful significance, so that, even if very restrictive, numerical solutions are still the best and more valuable sources of informations. It is quite possible that we know now very little more of the entire problem that was known to Poincare, with the advantage that we can now compute much faster and with much more precision. We feel that the papers collected in this Symposium have contributed a step forward to the comprehension of Resonance, Periodic Orbits and Stability. In a field like this, it would be a surprise if one had gone a long way toward that comprehension, during the short time of two weeks. But we are sure that the joint efforts of all the scientists involved has produced and will produce a measurable acceleration in the process. If this is true it will be a great satisfaction to us that this has happened in Brasil. The Southern Hemisphere in America has now begun to participate actively in the Astro­ nomical Society and for this, we are grateful to everyone who has helped.

The Trojan Manifold-Survey and Conjectures.- On Asymmetric Periodic Solutions of the Plane Restricted Problem of Three Bodies.- Two New Classes of Periodic Trojan Librations in the Elliptic Restricted Problem and Their Stabilities.- Minor Planets on Commensurable Orbits with Approaches to Jupiter.- Disintegration and Escape.- Secular Variations Determined by a Surface of Section.- On Bounded Solutions of the n-Body Problem.- Stability of Motion near Sun-Perturbed Earth-Moon Triangular Libration Points.- Motion near Sun Perturbed Earth-Moon Collinear Equilibrium Points (Status Report).- Resonances in the Elliptic Restricted Problem.- Numerical Studies of Solar Influenced Particle Motion near the Triangular Earth-Moon Libration Points.- On Using Minor Planets Close to the 2:1, 3:2, 4:3 Commensurabilities to Determine the Mass of Jupiter.- On the Relationship Between Comets and Minor Planets.- Absolute Orbits and Jupiter’s Great Satellites (Progress Report).- Existence of Periodic Solutions of Differential Equations of Second Order.- Sets of Collision Periodic Orbits in the Restricted Problem.- Periodic Orbits in Trigonometric Series.- Bifurcation Limits for the Existence of Periodic Orbits.- On the Accuracy in the Numerical Computation of Orbits.- On the Non-Existence of Transformations to Normal Form in Celestial Mechanics.- A Unified Treatment of Lunar Theory and Artificial Satellite Theory.- Stability of Free Rotation of a Rigid Body.- Wild Dynamical Systems, and the Role of Two or More Small Divisors.- The Planar Motion of a Trojan Asteroid.- On the Long-Term Evolution of Lunar Satellite Orbits.- Transient Annular Structures in Exploding Galaxies.- Resonance Phenomena in Spiral Galaxies.- On the Evolution of the Solar System and the Pluto-Neptune Case.- Flows near Isolated Invariant Sets in Dimension 3.- Dynamical Systems on Manifolds.- On a Criterion of Instability for Differential Equations with Time Delay.- The Libration Case of the Stellar Problem of Three Bodies.- Stability of Periodic Orbits in the Restricted Problem.- New Periodic Orbits in the General Problem of Three Bodies.- New Families of Periodic Orbits in the General Planar Problem of Three Bodies.- Stability and Resonances in the Restricted Problem.- Application of Hill’s Lunar Method in General Planetary Theory.- Stationary and Periodic Solutions for the Restricted Problem of Three Bodies in Three-Dimensional Space.- Motion of a Space Probe near an Oblate Planet.- On the Ideal Resonance Problem.- Parametric Resonance in Certain Nonlinear Systems.- Resonances in Duffing’s Problem.- Passage Through Resonance.- Two Centers of Libration.