Topics in Gravitational Dynamics

References......Page 0
Introduction......Page 9
Classical Integrable Systems......Page 11
Quasi--Integrable Systems and Hamiltonian Perturbation Theory......Page 15
Inside the Nekhoroshev Theorem......Page 21
Exponential Stability in Degenerate Systems......Page 27
References......Page 34
Introduction......Page 37
Arnold's Diffusion......Page 39
A Generalization of Arnold's Diffusion......Page 44
The Fast Lyapunov Indicator......Page 46
The Model Problem......Page 48
The FLI for Detecting the Geometry of Resonances......Page 49
Local and Global Arnold's Diffusion in the Convex Case......Page 51
Diffusion in Non-Convex Systems......Page 59
Conclusion......Page 70
References......Page 71
Introduction......Page 74
The Dissipative Standard Map......Page 75
Techniques for the Numerical Investigation of the Dynamics......Page 77
Adiabatic Invariants of the Pendulum......Page 83
A Paradigm from Celestial Mechanics: The Spin-Orbit Model......Page 84
The Restricted, Planar, Circular, Three-Body Problem......Page 90
Periodic Orbits for Non-Autonomous and Autonomous Systems......Page 91
References......Page 95
Introduction......Page 98
Connectance in Ecology: A Historical Perspective......Page 100
Connectance in Economics......Page 101
Linear Stability and Connectance: Basic Definitions......Page 103
The Diagonal Dominance Criterion and its Applicability......Page 104
The Stability Recovery Phenomenon: Some Simple Criteria......Page 107
The Influence of the Matrix Size......Page 113
Conclusions......Page 114
References......Page 115
Introduction......Page 117
Slow Dispersion of the Trojan Swarms......Page 121
Resonant Populations of Unstable Asteroids......Page 123
Chaotic Chronology of Asteroid Families......Page 129
Analytical Models of Chaotic Diffusion in MMRs......Page 133
Chaotic Transport in the Main Belt: A Numerical Survey......Page 144
Conclusions---Discussion......Page 151
References......Page 154
Introduction......Page 157
Theories of the Motion of Rotation of a Celestial Body......Page 159
Rotation of the Earth......Page 174
The Rotation of the Planets......Page 192
Conclusion......Page 209
References......Page 210
Introduction......Page 214
Multi-planet Systems......Page 216
Binary Systems......Page 219
Terrestrial Planets in Extra-Solar Planetary Systems......Page 227
Theoretical Considerations......Page 229
The G4 Terrestrial Planet in HD108874......Page 230
Concluding Remarks for Possible Terrestrial Planets......Page 232
References......Page 235
Introduction......Page 238
Eccentricity Observations......Page 240
Eccentricity Origin Theories......Page 241
Jet-Induced Excitation......Page 245
Concluding Remarks......Page 258
References......Page 259
Introduction......Page 262
Modelling the Stellar Pertubations......Page 263
Stellar Encounters......Page 265
The Dynamical Models......Page 266
Results......Page 270
References......Page 276
Introduction......Page 278
Models of Galactic Tide Effects on Cometary Orbits......Page 279
Comparisons Between the Different Models......Page 297
Hybrid Integrators......Page 298
Conclusion......Page 299
References......Page 300
Introduction......Page 302
Basic Notions......Page 304
The Statistical Mechanical Approach: Violent Relaxation......Page 327
The Orbital Approach: Global Dynamics and Self-Consistent Models of Galaxies......Page 352
The N-Body Approach......Page 369
References......Page 385
Introduction......Page 395
Solar Cycle Activity......Page 397
Tools......Page 402
Some Results......Page 404
Portrait of the Solar Activity Cycle in the Phases Space......Page 406
Conclusion......Page 408
References......Page 409
Index......Page 412