Dynamical Chaos in Planetary Systems

Preface
Contents
Part I Origins and Manifestations of Dynamical Chaos
	1 Chaotic Behaviour
		1.1 Pendulum, Resonances and Chaos
		1.2 Models of Resonance
		1.3 Interaction and Overlap of Resonances
		1.4 Symplectic Maps in General
		1.5 The Standard Map
		1.6 The Separatrix Map
		1.7 Generalized Separatrix Maps
		1.8 Geometry of Chaotic Layers
	2 Numerical Tools for Studies of Dynamical Chaos
		2.1 Lyapunov Exponents
		2.2 Fast Lyapunov Indicators
		2.3 MEGNO Charts
		2.4 Frequency Analysis
		2.5 Sections of Phase Space
		2.6 LCE Charts
		2.7 Poincaré Recurrences
	3 Lyapunov Timescales
		3.1 Chirikov's Constant
		3.2 Adiabatic Chaos
		3.3 Lyapunov Exponents in Resonance Doublets and Triplets
		3.4 Lyapunov Exponents in Resonance Multiplets
	4 Diffusion Timescales
		4.1 Diffusion Rates in Resonance Multiplets
		4.2 Diffusion Rates in Resonance Doublets
		4.3 Lyapunov and Diffusion Timescales: Relationships
		4.4 Two Kinds of Hamiltonian Intermittency
	5 Extents of Chaotic Domains
		5.1 The Separatrix Split
		5.2 Early Estimates of the Chaotic Layer Width
		5.3 The Layer Width in Case of Non-adiabatic Chaos
		5.4 The Layer Width in Case of Adiabatic Chaos
		5.5 Marginal Resonances in Case of Non-adiabatic Chaos
		5.6 Marginal Resonances in Case of Adiabatic Chaos
Part II Resonances and Chaos in the Solar System
	6 Defying the Orrery Paradigm: Historical Background
	7 Rotational Dynamics
		7.1 Rotational Dynamics of Satellites
			7.1.1 Hyperion and Other Chaotic Rotators
			7.1.2 Spin-Orbit Resonances
			7.1.3 Lyapunov Timescales of Chaotic Rotation
			7.1.4 Widths of Chaotic Layers
			7.1.5 Chaotic Planar Rotation and Chaotic Tumbling
			7.1.6 Stability with Respect to Tilting the Axis of Rotation
		7.2 Chaotic Obliquities of Planets
			7.2.1 Relevant Spin-Orbit Resonances
	8 Orbital Dynamics of Minor Bodies
		8.1 Dynamics of Satellite Systems
			8.1.1 The Miranda–Umbriel System
			8.1.2 Generalization of the Separatrix Algorithmic Map
			8.1.3 The Mimas–Tethys System
			8.1.4 The Prometheus–Pandora System
		8.2 Chaotic Dynamics of Asteroids and Kuiper Belt Objects
			8.2.1 Resonant Structure of the Asteroid Belt
			8.2.2 The Kuiper Belt Objects
			8.2.3 Two-Body Resonances
			8.2.4 Three-Body Resonances
			8.2.5 Secular Resonances
		8.3 Cometary Dynamics
			8.3.1 Comets: Highly Chaotic
			8.3.2 Lévy Flights at the Edge of Escape
		8.4 Dynamical Environments of Small Bodies
			8.4.1 Chaotic Zones Around Contact Binaries
			8.4.2 Ida and Dactyl
			8.4.3 Trans-Neptunian Objects, 2014 MU69 Among Them
	9 Orbital Dynamics of Planets
		9.1 Chaotic Giant Planets
Part III Dynamics of Exoplanets
	10 Exoplanets: An Overview
		10.1 History and Discoveries
		10.2 Definition of a Planet
		10.3 Typology and Properties of Exoplanets
			10.3.1 Mass Function and Mass-Radius Relationship
			10.3.2 Types of Exoplanets
			10.3.3 Physical Types of Planetary Systems
		10.4 Architecture and Dynamical Configurations
		10.5 Resonant and Multi-Resonant Systems
	11 Planetary Architecture: Stability, Packing and Ranging
		11.1 Stability Criteria
			11.1.1 Classical Results
			11.1.2 Wisdom's Criterion: The μ2/7 Law
			11.1.3 The Encounter Map
			11.1.4 The Two-Dimensional Encounter Map
			11.1.5 The Kepler Map Criterion: The μ2/5 Law
			11.1.6 Hill's Criterion: The μ1/3 Law
			11.1.7 The Holman–Wiegert Criteria
			11.1.8 Lyapunov and Escape Times: Linear and Quadratic Relationships
		11.2 Packing and Ranging Criteria
			11.2.1 Historical Background: Kepler's Goblet
			11.2.2 Dynamical Completeness
			11.2.3 The Moriwaki–Nakagawa Criterion
	12 Effects of Chaotic Clearing in Planetary Systems
		12.1 Close-to-Coorbital Clearing
		12.2 Circumbinary Clearing
		12.3 Resonant Clearings
		12.4 Inner Disintegration
	13 Multiplanet Systems of Single Stars
		13.1 Secular Planetary Dynamics
		13.2 Location and Interaction of Resonances
			13.2.1 The Outer Perturber Case
			13.2.2 The Inner Perturber Case
		13.3 Resonant and Formally Chaotic Exoplanet Systems
			13.3.1 The Kepler-223 System
			13.3.2 The Kepler-11 System
			13.3.3 The GJ-876 System
			13.3.4 The Kepler-36 System
			13.3.5 The HD 12661 System
	14 Planetary Systems of Multiple Stars
		14.1 Circum-Companion Systems
			14.1.1 The α Centauri System
			14.1.2 The υ Andromedae System
			14.1.3 The 55 Cancri System
			14.1.4 The 16 Cygni System
		14.2 Circumbinary Systems
			14.2.1 Kepler's Circumbinary Planets
			14.2.2 Migration and Chaos as System Architects
			14.2.3 Chaotic Zones
			14.2.4 Structure of Chaos Border
			14.2.5 The Mass Parameter Threshold
	15 The Lidov–Kozai Effect: Chaotic Implications
		15.1 Multiplanet Systems
		15.2 Planetary Systems of Binary Stars
		15.3 Chaos Due to the Lidov–Kozai Effect
	16 Epilogue
A Basic Notations
	List of Abbreviations
B Astronomical Constants and Parameters
C The Melnikov–Arnold Integrals
Bibliography
Index