Periodic Orbits, Stability and Resonances: 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

Front Matter....Pages I-XIV
The Trojan Manifold — Survey and Conjectures....Pages 1-18
On Asymmetric Periodic Solutions of the Plane Restricted Problem of Three Bodies....Pages 19-32
Two New Classes of Periodic Trojan Librations in the Elliptic Restricted Problem and Their Stabilities....Pages 33-44
Minor Planets on Commensurable Orbits with Approaches to Jupiter....Pages 45-52
Disintegration and Escape....Pages 53-55
Secular Variations Determined by a Surface of Section....Pages 56-75
On Bounded Solutions of the n -Body Problem....Pages 76-81
Stability of Motion Near Sun-Perturbed Earth-Moon Triangular Libration Points....Pages 82-90
Motion Near Sun Perturbed Earth-Moon Collinear Equilibrium Points....Pages 91-95
Resonances in the Elliptic Restricted Problem....Pages 96-127
Numerical Studies of Solar Influenced Particle Motion Near the Triangular Earth-Moon Libration Points....Pages 128-142
On Using Minor Planets Close to the 2:1, 3:2, 4:3 Commensurabilities to Determine the Mass of Jupiter....Pages 143-150
On the Relationship Between Comets and Minor Planets....Pages 151-163
Absolute Orbits and Jupiter’s Great Satellites....Pages 164-167
Existence of Periodic Solutions of Differential Equations of Second Order....Pages 168-175
Sets of Collision Periodic Orbits in the Restricted Problem....Pages 176-191
Periodic Orbits in Trigonometric Series....Pages 192-209
Bifurcation Limits for the Existence of Periodic Orbits....Pages 210-215
On the Accuracy in the Numerical Computation of Orbits....Pages 216-227
On the Non-Existence of Transformations to Normal form in Celestial Mechanics....Pages 228-231
A Unified Treatment of Lunar Theory and Artificial Satellite Theory....Pages 232-258
Stability of Free Rotation of a Rigid Body....Pages 259-271
Wild Dynamical Systems, and the Role of Two or More Small Divisors....Pages 272-285
The Planar Motion of a Trojan Asteroid....Pages 286-303
On the Long-Term Evolution of Lunar Satellite Orbits....Pages 304-313
Transient Annular Structures in Exploding Galaxies....Pages 314-321
Resonance Phenomena in Spiral Galaxies....Pages 322-327
On the Evolution of the Solar System and the Pluto-Neptune Case....Pages 328-331
Flows Near Isolated Invariant Sets in Dimension 3....Pages 332-336
Dynamical Systems on Manifolds....Pages 337-338
On a Criterion of Instability for Differential Equations with Time Delay....Pages 339-342
The Libration Case of the Stellar Problem of Three Bodies....Pages 343-348
Stability of Periodic Orbits in the Restricted Problem....Pages 349-374
New Periodic Orbits in the General Problem of Three Bodies....Pages 375-381
New Families of Periodic Orbits in the General Planar Problem of Three Bodies....Pages 382-396
Stability and Resonances in the Restricted Problem....Pages 397-409
Application of Hill’s Lunar Method in General Planetary Theory....Pages 410-450
Stationary and Periodic Solutions for the Restricted Problem of Three Bodies in Three-Dimensional Space....Pages 451-468
Motion of a Space Probe Near an Oblate Planet....Pages 469-473
On the Ideal Resonance Problem....Pages 474-481
Parametric Resonance in Certain Nonlinear Systems....Pages 482-492
Resonances in Duffing’s Problem....Pages 493-500
Passage Through Resonance....Pages 501-514
Two Centers of Libration....Pages 515-530