Topics in Gravitational Dynamics: Solar, Extra-Solar and Galactic Systems

✍ Scribed by Daniel Benest; Claude Froeschle; Elena Lega

• Publisher: Springer
• Year: 2007
• Tongue: English
• Leaves: 423
• Category: Library

✦ Synopsis

This set of lectures collects surveys of open problems in celestial dynamics and dynamical astronomy applied to solar, extra-solar and galactic systems. The discovery and thus the possibility to study many new extra-solar planetary systems have spurred new developments in the field and enabled the testing and enlargement of the domains of validity of theoretical predictions through the Nekhoroshev theorem.

✦ Table of Contents

Lecture Notes in Physics 729
Topics in Gravitational Dynamics
Preface
Contents
1 An Overview on the Nekhoroshev Theorem. Massimiliano Guzzo
1.1 Introduction
1.2 Classical Integrable Systems
1.3 Quasi–Integrable Systems and Hamiltonian Perturbation Theory
1.4 Inside the Nekhoroshev Theorem
1.5 Exponential Stability in Degenerate Systems
References
2 Diffusion in Hamiltonian Quasi-Integrable Systems. Elena Lega, Claude Froeschlé and Massimiliano Guzzo
2.1 Introduction
2.2 Arnold’s Diffusion
2.3 A Generalization of Arnold’s Diffusion
2.4 The Fast Lyapunov Indicator
2.5 The Model Problem
2.6 The FLI for Detecting the Geometry of Resonances
2.7 Local and Global Arnold’s Diffusion in the Convex Case
2.8 Diffusion in Non-Convex Systems
2.9 Conclusion
References
3 Weakly Dissipative Systems in Celestial Mechanics. Alessandra Celletti
3.1 Introduction
3.2 The Dissipative Standard Map
3.3 Techniques for the Numerical Investigation of the Dynamics
3.4 Adiabatic Invariants of the Pendulum
3.5 A Paradigm from Celestial Mechanics: The Spin-Orbit Model
3.6 The Restricted, Planar, Circular, Three-Body Problem
3.7 Periodic Orbits for Non-Autonomous and Autonomous Systems
References
4 Connectance and Stability of Dynamical Systems. Marina Cosentino, Dimitri Laveder, Elena Lega and Claude Froeschlé
4.1 Introduction
4.2 Connectance in Ecology: A Historical Perspective
4.3 Connectance in Economics
4.4 Linear Stability and Connectance: Basic Definitions
4.5 The Diagonal Dominance Criterion and its Applicability
4.6 The Stability Recovery Phenomenon: Some Simple Criteria
4.7 The Influence of the Matrix Size
4.8 Conclusions
References
5 Chaotic Diffusion of Asteroids. Kleomenis Tsiganis
5.1 Introduction
5.2 Slow Dispersion of the Trojan Swarms
5.3 Resonant Populations of Unstable Asteroids
5.4 Chaotic Chronology of Asteroid Families
5.5 Analytical Models of Chaotic Diffusion in MMRs
5.6 Chaotic Transport in the Main Belt: A Numerical Survey
5.7 Conclusions—Discussion
References
6 An Overview of the Rotations of Planets in the Solar System. Jean Souchay
6.1 Introduction
6.2 Theories of the Motion of Rotation of a Celestial Body
6.3 Rotation of the Earth
6.4 The Rotation of the Planets
6.5 Conclusion
References
7 On the Stability of Extra-Solar Planetary Systems. Elke Pilat-Lohinger and Rudolf Dvorak
7.1 Introduction
7.2 Multi-planet Systems
7.3 Binary Systems
7.4 Terrestrial Planets in Extra-Solar Planetary Systems
7.5 Theoretical Considerations
7.6 Gl 777 A
7.7 The G4 Terrestrial Planet in HD108874
7.8 Concluding Remarks for Possible Terrestrial Planets
References
8 Origin Theories for the Eccentricities of Extrasolar Planets. Fathi Namouni
8.1 Introduction
8.2 Eccentricity Observations
8.3 Eccentricity Origin Theories
8.4 Jet-Induced Excitation
8.5 Concluding Remarks
References
9 Methods for the Study of the Dynamics of the Oort Cloud Comets I: Modelling the Stellar Perturbations. Marc Fouchard, Christiane Froeschlé, Hans Rickman and Giovanni B. Valsecchi
9.1 Introduction
9.2 Modelling the Stellar Pertubations
9.3 Stellar Encounters
9.4 The Dynamical Models
9.5 Results
9.6 Conclusions
References
10 Methods for the Study of the Dynamics of the Oort Cloud Comets II: Modelling the Galactic Tide. Marc Fouchard, Christiane Froeschlé, Sławomir Breiter, Roman Ratajczak, Giovanni B. Valsecchi and Hans Rickman
10.1 Introduction
10.2 Models of Galactic Tide Effects on Cometary Orbits
10.3 Comparisons Between the Different Models
10.4 Hybrid Integrators
10.5 Conclusion
References
11 Special Features of Galactic Dynamics. Christos Efthymiopoulos, Nikos Voglis† and C. Kalapotharakos
11.1 Introduction
11.2 Basic Notions
11.3 The Statistical Mechanical Approach: Violent Relaxation
11.4 The Orbital Approach: Global Dynamics and Self-Consistent Models of Galaxies
11.5 The N-Body Approach
References
12 On the Difficulty to Foresee Solar Cycles: A Non-Deterministic Approach. Jean-Pierre Rozelot
12.1 Introduction
12.2 Solar Cycle Activity
12.3 Tools
12.4 Some Results
12.5 Portrait of the Solar Activity Cycle in the Phases Space
12.6 Conclusion
References
Index