Dynamics Reported Dynamics Reported

Dynamics Reported reports on recent developments in dynamical systems theory. Dynamical systems theory of course originated from ordinary differential equations. Today, dynamical systems theory covers a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems theory has evolved remarkably rapidly in the recent years. A wealth of new phenomena, new ideas and new techniques proved to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications have appeared and still will appear. Dynamics Reported presents carefully written articles on major subjects in dynamical systems and their applications, addressed not only to specialists but also to a broader range of readers. Topics are advanced while detailed exposition of ideas, restriction to typical results, rather than to the most general ones, and last but not least lucid proofs help to gain an utmost degree of clarity. It is hoped that Dynamics Reported will stimulate exchange of ideas among those working in dynamical systems and moreover will be useful for those entering the field.

1 Mather Sets for Twist Maps and Geodesics on Tori.- 2 Connecting Orbits in Scalar Reaction Diffusion Equations.- 3 Qualitative Theory of Nonlinear Resonance by Averaging and Dynamical Systems Methods.- 4 An Algorithmic Approach for Solving Singularly Perturbed Initial Value Problems.- 5 Exponential Dichotomies, the Shadowing Lemma and Transversal Homoclinic Points.