Jones, C.K.R.T. (ed.)
Kirchgraber, U. (ed.)
Walther, H.O. (ed.)
|Title||Dynamics Reported (New Series), vol. I|
|Year of publication||1992|
|Reviewed by||Paul A. Blaga|
This is the first volume of a new series of "Dynamics Reported", presenting review articles on major subjects in dynamical systems and their applications.
The present issue of the series includes six papers, which will be shortly described in the following. The first oontribution ("Bifurcational Aspects of Parametric Resonance", by H.W. Broer and G. Vegter) presents a study of Hamiltonian nonlinear oscillators with parametric forcing. The second one ("A Survey of Normalization Techniques Applied to Perturbed Keplerian Systems", by R. Cushman) illustrates the use of normal form techniques in the study of Hamiltonian perturbations of the two-body problem in the three-space, applying these techniques also to some concrete problems. The following paper ("On Littlewood's Counterexemple of Unbounded Motions In Superquadratic Potentials", by M. Levi) provides a simplified proof of the existence of unbounded motions for a conservative system describing the motion in a superlinear potential with periodic forcing. The fourth article ("Center Manifold Theory in Infinite Dimensions", by A. Vanderbauwhede and G. Iooss) gives an approach to center manifolds in infinite-dimensional systems. There are given examples related to Navier-Stokes equations. The fifth work ("Oscillations in Singularly Perturbed Delay Equstions", by A.F. Ivanov and A.N. Sharkovsky) contains some basic relations between the dynamics of interval maps and perturbations of differential delay equations, while the last one ("Topological Approach to Differential Inclusions on Closed Subsets of R^n", by R. Bielawski, L. Górnewicz and S. Plascacz) presents a survey of the new results on existence, periodicity and topological properties of the solution sets. The papers are excellent written, are self-contained and are addressed not only to specialists, but also to graduate students. The book is valuable for anyone who wish to be acquainted with the new results and methods of dynamical systems theory. There are list of references after each paper, but there is no index.