Dynamics Reported

Bifurcational Aspects of Parametric Resonance.- 1. Setting of the Problem.- 2. A Normal Form Theory.- 3. Computation of a Third-Order Normal Form.- 4. The Planar Hamilton Form.- 5. Dynamical Conclusions.- A Survey of Normalization Techniques Applied to Perturbed Keplerian Systems.- 1. Introduction.- 2. Perturbed Keplerian Systems.- 3. Normal Form: Theory.- 4. Normal Form: Practice.- 5. Reduction to One Degree of Freedom.- 6. Analysis of Normalized Hamiltonian.- 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.- References.- Center Manifold Theory in Infinite Dimensions.- 1. Introduction.- 2. General Theory.- 3. Spectral Theory.- 4. Examples.- 5. Application to Hydrodynamic Stability Problems.- 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.

Dynamics Reported is a series of books covering recent research in the mathematics of dynamical systems. The style is expository, but at the research level. Roughly one book per year is planned. The material is ideally suited to be the foundation of seminars on dynamical systems, involving advanced students and active mathematicians.