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For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.

Celestial mechanics. --- Accuracy and precision. --- Action-angle coordinates. --- Analytic function. --- Bounded variation. --- Calculation. --- Chaos theory. --- Coefficient. --- Commutator. --- Constant term. --- Continuous embedding. --- Continuous function. --- Coordinate system. --- Countable set. --- Degrees of freedom (statistics). --- Degrees of freedom. --- Derivative. --- Determinant. --- Differentiable function. --- Differential equation. --- Dimension (vector space). --- Discrete group. --- Divergent series. --- Divisor. --- Duffing equation. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Elliptic orbit. --- Energy level. --- Equation. --- Ergodic theory. --- Ergodicity. --- Euclidean space. --- Even and odd functions. --- Existence theorem. --- Existential quantification. --- First-order partial differential equation. --- Forcing function (differential equations). --- Fréchet derivative. --- Gravitational constant. --- Hamiltonian mechanics. --- Hamiltonian system. --- Hessian matrix. --- Heteroclinic orbit. --- Homoclinic orbit. --- Hyperbolic partial differential equation. --- Hyperbolic set. --- Initial value problem. --- Integer. --- Integrable system. --- Integration by parts. --- Invariant manifold. --- Inverse function. --- Invertible matrix. --- Iteration. --- Jordan curve theorem. --- Klein bottle. --- Lie algebra. --- Linear map. --- Linear subspace. --- Linearization. --- Maxima and minima. --- Monotonic function. --- Newton's method. --- Nonlinear system. --- Normal bundle. --- Normal mode. --- Open set. --- Parameter. --- Partial differential equation. --- Periodic function. --- Periodic point. --- Perturbation theory (quantum mechanics). --- Phase space. --- Poincaré conjecture. --- Polynomial. --- Probability theory. --- Proportionality (mathematics). --- Quasiperiodic motion. --- Rate of convergence. --- Rational dependence. --- Regular element. --- Root of unity. --- Series expansion. --- Sign (mathematics). --- Smoothness. --- Special case. --- Stability theory. --- Statistical mechanics. --- Structural stability. --- Symbolic dynamics. --- Symmetric matrix. --- Tangent space. --- Theorem. --- Three-body problem. --- Uniqueness theorem. --- Unitary matrix. --- Variable (mathematics). --- Variational principle. --- Vector field. --- Zero of a function.

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The description for this book, Contributions to the Theory of Games (AM-24), Volume I, will be forthcoming.

Game theory. --- Affine space. --- Almost surely. --- Banach space. --- Basic solution (linear programming). --- Bilinear form. --- Boundary (topology). --- Bounded variation. --- Calculation. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Coefficient. --- Combination. --- Completeness of the real numbers. --- Computation. --- Computational problem. --- Connected space. --- Continuous function (set theory). --- Continuous function. --- Continuous game. --- Convex combination. --- Convex set. --- Counterexample. --- Diagram (category theory). --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Elementary proof. --- Equation solving. --- Equilibrium point. --- Euclidean space. --- Existential quantification. --- Exterior (topology). --- Extreme point. --- Facet (geometry). --- Fubini's theorem. --- Function (mathematics). --- Function space. --- Fundamental theorem. --- Geometry. --- Helly's theorem. --- Hyperplane. --- Identity matrix. --- Inequality (mathematics). --- Infimum and supremum. --- Interior (topology). --- Invertible matrix. --- Iterative method. --- Limit of a sequence. --- Limit point. --- Linear inequality. --- Linear map. --- Linear programming. --- Mathematical analysis. --- Mathematical optimization. --- Mathematics. --- Matrix (mathematics). --- Maxima and minima. --- Maximal set. --- Measure (mathematics). --- Minimax theorem. --- Mutual exclusivity. --- NSPACE. --- Orthogonal basis. --- Orthogonal matrix. --- Orthogonal polynomials. --- Partially ordered set. --- Permutation. --- Polyhedron. --- Polynomial. --- Probability distribution. --- Probability. --- Proportionality (mathematics). --- Rational number. --- Riemann–Stieltjes integral. --- Scientific notation. --- Set (mathematics). --- Set theory. --- Sign (mathematics). --- Skew-symmetric matrix. --- Solution concept. --- Special case. --- Strategy (game theory). --- Subsequence. --- Subset. --- Summation. --- Symmetrization. --- Theorem. --- Theory of Games and Economic Behavior. --- Theory. --- Topology. --- Transfinite number. --- Transfinite. --- Unit interval. --- Unit sphere. --- Unit vector. --- Vandermonde matrix. --- Variable (mathematics). --- Vector space. --- Weak convergence (Hilbert space). --- Weyl's theorem.