4 Variational Principles and Methods
4．1 Geometry of Regions of Possible Motion
4．1．1 Principle of Stationary Abbreviated Action
4．1．2 Geometry of a Neighbourhood of the Boundary
4．1．3 Riemannian Geometry of Regions of Possible Motion with Boundary
4．2 Periodic Trajectories of Natural Mechanical Systems
4．2．1 Rotations and Librations
4．2．2 Librations in Non-Simply-Connected Regions of Possible Motion
4．2．3 Librations in Simply Connected Domains and Seifert's Conjecture
4．2．4 Periodic Oscillations of a Multi-Link Pendulum
4．3 Periodic Trajectories of Non-Reversible Systems
4．3．1 Systems with Gyroscopic Forces and Multivalued Functionals
4．3．2 Applications of the Generalized Poincare Geometric Theorem
4．4 Asymptotic Solutions． Application to the Theory of Stability of Motion
4．4．1 Existence of Asymptotic Motions
4．4．2 Action Function in a Neighbourhood of an Unstable Equilibrium Position
4．4．3 Instability Theorem
4．4．4 Multi-Link Pendulum with Oscillating Point of Suspension
4．4．5 Homoclinic Motions Close to Chains of Homoclinic Motions

5 Integrable Systems and Integration Methods
5．1 Brief Survey of Various Approaches to Integrability of Hamiltonian Systems
5．1．1 Quadratures
5．1．2 Complete Integrability
5．1．3 Normal Forms
5．2 Completely Integrable Systems
5．2．1 Action-Angle Variables
5．2．2 Non-Commutative Sets of Integrals
5．2．3 Examples of Completely Integrable Systems
5．3 Some Methods of Integration of Hamiltonian Systems
5．3．1 Method of Separation of Variables
5．3．2 Method of L-A Pairs
5．4 Integrable Non-Holonomic Systems
5．4．1 Differential Equations with Invariant Measure
5．4．2 Some Solved Problems of Non-Holonomic Mechanics

6 Perturbation Theory for Integrable Systems
6．1 Averaging of Perturbations
6．1．1 Averaging Principle
6．1．2 Procedure for Eliminating Fast Variables． Non-Resonant Case
6．1．3 Procedure for Eliminating Fast Variables． ResonantCase
6．1．4 Averaging in Single-Frequency Systems
6．1．5 Averaging inSystems with Constant Frequencies ．．．
6．1．6 Averaging in Non-Resonant Domains
6．1．7 Effect of a Single Resonance
6．1．8 Averaging in Two-Frequency Systems
6．1．9 Averaging in Multi-Frequency Systems
6．1．10 Averaging at Separatrix Crossing
6．2 Averaging in Hamiltonian Systems
6．2．1 Application of the Averaging Principle
6．2．2 Procedures for Eliminating Fast Variables
6．3 KAM Theory
6．3．1 Unperturbed Motion． Non-Degeneracy Conditions
6．3．2 Invariant Tori of the Perturbed System
6．3．3 Systems with Two Degrees of Freedom
6．3．4 Diffusion of Slow Variables in Multidimensional
Systems and its Exponential Estimate
6．3．5 Diffusion without Exponentially Small Effects
6．3．6 Variants of the Theorem on Invariant Tori
6．3．7 KAM Theory for Lower-Dimensional Tori
6．3．8 Variational Principle for Invariant Tori． Cantori
6．3．9 Applications of KAM Theory
6．4 Adiabatic Invariants
6．4．1 Adiabatic Invariance of the Action Variable in Single-Frequency Systems
……

7 Non-Integrable Systems
8 Theory of Small Oscillations
9 Tensor Invariants of Equations of Dynamics

Recommended Reading
Bibliography
Index of Names
Subject Index

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