Bifurcational Aspects of Parametric Resonance.- 1. Setting of the Problem.- a. Introduction.- b. The Parametrically Forced Pendulum, Motivation.- c. Setting of the Problem, Outline of the Method.- 2. A Normal Form Theory.- a. Preliminaries.- b. Subharmonics: A Covering Space and Discrete Symmetry.- c. The Normal Form.- 3. Computation of a Third-Order Normal Form.- 4. The Planar Hamilton Form.- a. Introduction.- b. The Type of the Origin as a Singularity, Part of the Bifurcation Diagram.- c. Bifurcations in the Case ak?0.- d. Some Remarks on a Case of Small ak?0.- e. Nearby Higher Order Subharmonics.- 5. Dynamical Conclusions.- a. (Sub-) harmonics and Their Invariant Manifolds.- b. Quasi-Periodic Invariant Circles.- c. Miscellaneous Remarks.- References.- A Survey of Normalization Techniques Applied to Perturbed Keplerian Systems.- 1. Introduction.- 2. Perturbed Keplerian Systems.- 2.1 Basic Definitions.- 2.2 Quadratic Zeeman Effect.- 2.3 Orbiting Dust.- 2.4 A Lunar Problem.- 2.5 The Artificial Satellite.- 3. Normal Form: Theory.- 3.1 Regularization.- 3.2 Lie Series and Normal Form.- 3.3 Constrained Normal Form.- 4. Normal Form: Practice.- 4.1 Extensions to a Constrained System.- 4.2 Normal Form for the Quadratic Zeeman Effect.- 4.3 Other Examples of Constrained Normal Form.- 4.4 Normalization of the Reduced Hamiltonian.- 4.5 Normal Form and Symmetry.- 5. Reduction to One Degree of Freedom.- 5.1 Reduction of the Keplerian Symmetry.- 5.2 Reduction of the Axial Symmetry.- 6. Analysis of Normalized Hamiltonian.- 6.1 The Second Reduced Hamiltonian.- 6.2 Level Sets of Hl,c: I.- 6.3 Singular Toral Fibration: I.- 6.4 Level Sets of KL,HII.- 6.5 Singular Toral Fibration: II.- 7. Appendix 1.- 8. Appendix 2.- References.- On Littlewood's Counterexample of Unbounded Motions in Superquadratic Potentials.- 1. Introduction.- 2. Results.- 3. Proof of the Theorem.- 3.1 An Outline of the Construction.- 3.2 Modification of the Potential.- 3.3 Proof of the Resonance Condition.- 3.4 End of the Proof of the Theorem.- 3.5 Proof of Lemma 1.- 3.6 Proof of Lemma 2.- 3.7 Appendix: An Alternative Proof of the Estimate on ?(0).- References.- Center Manifold Theory in Infinite Dimensions.- 1. Introduction.- 2. General Theory.- 2.1 Main Theorems.- 2.2 Special Cases.- 3. Spectral Theory.- 4. Examples.- 5. Application to Hydrodynamic Stability Problems.- 5.1 The Classical Navier-Stokes Equations.- 5.2 Stationary Navier-Stokes Equations in a Cylinder.- References.- Oscillations in Singularly Perturbed Delay Equations.- 1. Difference Equations.- 2. Singular Perturbations of Difference Equations with Continuous Argument: Simplest Properties.- 3. Continuous Dependence on a Paramete.- 4. Impact of Singular Perturbations: Examples.- 5. Attractors of Interval Maps and Asymptotic Behavior of Solutions.- 6. Existence of Periodic Solutions.- 7. Concluding Remarks and Open Questions.- References.- Topological Approach to Differential Inclusions on Closed Subsets of ?n.- 1. Multivalued Mappings.- 2. Topological Degree of Admissible Mappings in ?n.- 3. Aronszajn's Result.- 4. Selectionable and ?-Selectionable Multivalued Maps.- 5. Differential Inclusions in ?n.- 6. Periodic Solutions of Differential Inclusions in ?n.- 7. Sets with Property p.- 8. Contingent Cone Valued Maps.- 9. Differential Inclusions on Sets with Property p.- 10. Proof of Lemma (7.3).- References.