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035   $a(OCoLC)979633883
035   $a(DE-B1597)9781400882694
035   $a(EXLCZ)993710000000628091
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aStable and Random Motions in Dynamical Systems $eWith Special Emphasis on Celestial Mechanics (AM-77) /$fJurgen Moser
205   $aWith a New foreword by Philip J. Holmes
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©2001
215   $a1 online resource (212 pages) $cillustrations
225 0 $aPrinceton Landmarks in Mathematics and Physics ;$v77
300   $a"The Institute for Advanced Study."
311   $a0-691-08910-8 
320   $aIncludes bibliographical references.
327   $tFrontmatter -- $tTABLE OF CONTENTS -- $tI. INTRODUCTION -- $tII. STABILITY PROBLEMS -- $tIII. STATISTICAL BEHAVIOR -- $tV. FINAL REMARKS -- $tV. EXISTENCE PROOF IN THE PRESENCE OF SMALL DIVISORS -- $tVI. PROOFS AND DETAILS FOR CHAPTER III -- $tBOOKS AND SURVEY ARTICLES
330   $aFor centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.
410  0$aPrinceton landmarks in mathematics and physics.
410  0$aHermann Weyl lectures.
606   $aCelestial mechanics
610   $aAccuracy and precision.
610   $aAction-angle coordinates.
610   $aAnalytic function.
610   $aBounded variation.
610   $aCalculation.
610   $aChaos theory.
610   $aCoefficient.
610   $aCommutator.
610   $aConstant term.
610   $aContinuous embedding.
610   $aContinuous function.
610   $aCoordinate system.
610   $aCountable set.
610   $aDegrees of freedom (statistics).
610   $aDegrees of freedom.
610   $aDerivative.
610   $aDeterminant.
610   $aDifferentiable function.
610   $aDifferential equation.
610   $aDimension (vector space).
610   $aDiscrete group.
610   $aDivergent series.
610   $aDivisor.
610   $aDuffing equation.
610   $aEigenfunction.
610   $aEigenvalues and eigenvectors.
610   $aElliptic orbit.
610   $aEnergy level.
610   $aEquation.
610   $aErgodic theory.
610   $aErgodicity.
610   $aEuclidean space.
610   $aEven and odd functions.
610   $aExistence theorem.
610   $aExistential quantification.
610   $aFirst-order partial differential equation.
610   $aForcing function (differential equations).
610   $aFréchet derivative.
610   $aGravitational constant.
610   $aHamiltonian mechanics.
610   $aHamiltonian system.
610   $aHessian matrix.
610   $aHeteroclinic orbit.
610   $aHomoclinic orbit.
610   $aHyperbolic partial differential equation.
610   $aHyperbolic set.
610   $aInitial value problem.
610   $aInteger.
610   $aIntegrable system.
610   $aIntegration by parts.
610   $aInvariant manifold.
610   $aInverse function.
610   $aInvertible matrix.
610   $aIteration.
610   $aJordan curve theorem.
610   $aKlein bottle.
610   $aLie algebra.
610   $aLinear map.
610   $aLinear subspace.
610   $aLinearization.
610   $aMaxima and minima.
610   $aMonotonic function.
610   $aNewton's method.
610   $aNonlinear system.
610   $aNormal bundle.
610   $aNormal mode.
610   $aOpen set.
610   $aParameter.
610   $aPartial differential equation.
610   $aPeriodic function.
610   $aPeriodic point.
610   $aPerturbation theory (quantum mechanics).
610   $aPhase space.
610   $aPoincaré conjecture.
610   $aPolynomial.
610   $aProbability theory.
610   $aProportionality (mathematics).
610   $aQuasiperiodic motion.
610   $aRate of convergence.
610   $aRational dependence.
610   $aRegular element.
610   $aRoot of unity.
610   $aSeries expansion.
610   $aSign (mathematics).
610   $aSmoothness.
610   $aSpecial case.
610   $aStability theory.
610   $aStatistical mechanics.
610   $aStructural stability.
610   $aSymbolic dynamics.
610   $aSymmetric matrix.
610   $aTangent space.
610   $aTheorem.
610   $aThree-body problem.
610   $aUniqueness theorem.
610   $aUnitary matrix.
610   $aVariable (mathematics).
610   $aVariational principle.
610   $aVector field.
610   $aZero of a function.
615  0$aCelestial mechanics.
676   $a521/.1
700   $aMoser$b Jurgen, $040546
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910164944903321
996   $aStable and random motions in dynamical systems$9334062
997   $aUNINA