This book provides a brief introduction to some basic but important problems in celestial mechanics, and particularly in the few-body problem, such as the permissible and forbidden region of motion, the evolution of moment of inertia of a system, and the orbital stability of asteroids in the solar system. All these are based on some main results in the authors' research works, which are related to the qualitative method of celestial mechanics and nonlinear dynamics. Some of these works are interdisciplinary, involving celestial mechanics, nonlinear dynamics and other disciplines. The book covers a variety of topics for dynamics in the solar system, including the comets, asteroids, planetary rings, Trojan asteroids, etc.
As a senior scientist, Professor Sun shares his research experiences in this book. Readers may find plenty of information both about the theoretical and numerical analyses in celestial mechanics, and about the applications of theories and methods to dynamical problems in astronomy.
Qualitative Analyses on Motion in 3-Body System:
Equations of Motion and Invariants
Condition of Permissible Motion
Variations of Configuration and Position
Restricted 3-Body Problem and Singular Points of Motion
Stabilities of Lagrange and Euler Solutions
Elliptic Restricted 3-Body Problem
Hill Region in 3-Body Problem
Evolution of Inertia Momentum in N-Body Problem
Motion of Isolated Body in 3-Body Problem
Sitnikov Motion and Its Generalization
Central Configuration of 4-Body Problem
Central Configuration of N-Body Problem with General Attraction and Homographic Solutions
Motion of Small Bodies in the Planetary System:
Mapping Method in Hamiltonian System
Structure of Phase Space Near Lagrange Solutions
Stability of Asteroid Orbits in Resonances
Shepherding of Uranian Ring
Formation of Kuiper Belt
Dynamics of Neptune Trojans
Apsidal and Nodal Resonances in Multiple
Aspidal Corotation in 3:1 Mean Motion Resonance
Chaotic Motion of Orbits:
Conservative Dynamical System
Ordered and Chaotic Motion
Poincare Surface of Section
Ordered and Chaotic Motion of Stars
Application of Mapping Method to Comet Motion
Global Applicability of Symplectic Integrator
Transfer of Comet Orbit
Random Walk in Comet Motion
Chaotic Region of Encounter-Type Orbit
Orbit Diffusion:
Diffusion in Comet Motion
KS Entropy of Area-Preserving Mapping
Invariant Tori in Volume-Preserving Mapping
Perturbed Extension of Area-Preserving Mapping
KS Entropy of Volume-Preserving Mapping
Attractor in Three-Dimension Mapping
Stickiness Effect and Hyperbolic Structure (I)
Stickiness Effect and Hyperbolic Structure (II)
Diffusion in Four-Dimensional Mapping
420pp Dec 2015
ISBN: 978-981-4630-54-2 (hardcover)
Series on Knots and Everything: Forthcoming
This invaluable book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects.
Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.
Introduction
Preliminaries
Filling Dehn Surfaces
Johansson Diagrams
Covering Spaces
Filling Homotopies
Diagram Moves
Miscellany
Readership: Graduate students and researchers interested in low-dimensional topology.
350pp May 2016
ISBN: 978-981-4725-48-4 (hardcover)
This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics.
Algebra, Logic and Combinatorics is the third volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.
Introduction to the Finite Simple Groups (Robert Wilson)
The Invariant Theory of Finite Groups (Peter Fleischmann and Jim Shank)
Introduction to Representations of Algebras and Quivers (Anton Cox)
Model Theory (Ivan Tomasi?)
Enumerative Combinatorics (Peter Cameron)
Readership: Researchers, graduate or PhD mathematical-science students who require a reference book that covers algebra, logic or combinatorics.
180pp Jul 2016
ISBN: 978-1-78634-029-0 (hardcover)
USD75.00 Buy Now
ISBN: 978-1-78634-030-6 (softcover)
USD38.00 Buy No
Series on Knots and Everything: Forthcoming
The first volume, Geometry, Language and Strategy, extended the concepts of Game Theory, replacing static equilibrium with a deterministic dynamic theory. The first volume opened up many applications that were only briefly touched on. To study the consequences of the deterministic approach in contrast to standard Bayesian approaches, the richness of applications, requires an engineering foundation and discipline, which this volume supplies. It provides a richer list of applications, such as the Prisoner's Dilemma, which extends the resonant behavior of Vol. 1 to more general time-dependent and transient behaviors.
Physical and Game Theory Foundations
Dynamics of Decision Processes
Inertial Behaviors
Persistent Behaviors
Deconstructing the Theory
Steady-State Harmonics
Prisoner's Dilemma: A Code of Conduct Application
Prisoner's Dilemma: Steady-State Geometry
Prisoner's Dilemma: Determinism and Chaos
Robinson Crusoe Economics
Short Historical Review of Game Theory
Decisions and Determinism
Global System View
Vorticity with Multiple Active Strategies
Three Dimensional Models
Two-Strategy Two-Person Decision Processes
Physical Distinctions for Decision Processes
Social Distinctions for Decision Processes
Readership: Researchers in game theory, optimization and control theory, fluid mechanics, electrical engineering.
850pp Aug 2016
ISBN: 978-981-4719-92-6 (hardcover)