Russian Mathematical Surveys · 1992 · 190 citations · 33 references
Numerical AnalysisEngineeringPerturbation MethodSingularly Perturbed ProblemRobust ToriCelestial MechanicsKam TheoryCanonical Perturbation TheoryBifurcation TheoryGeometric Singular Perturbation TheoryFunctional AnalysisApproximation TheoryPeriodic Toruschapter IiiStability
CONTENTSChapter I. IntroductionChapter II. Stability in the neighbourhood of a periodic torusChapter III. Stability for arbitrary initial conditionsChapter IV. Transpositions, applications, prospects §1. Additional variables and an application to celestial mechanics §2. Transposition to other contexts and degenerate cases §3. Systems with (infinitely) many degrees of freedom §4. Steepness, quasi-convexity, and closed orbitsChapter V. Robust tori; Arnol'd diffusion §1. Robust tori and normalization §2. Arnol'd diffusionAppendix 1. Some Diophantine approximationAppendix 2. Gevrey asymptotic expansionsReferences
33