March  2008, 9(3&4, May): i-ii. doi: 10.3934/dcdsb.2008.9.3i

Preface

1. 

Università di Firenze, Dipartimento di Sistemi e Informatica, Via Santa Marta 3, 50139 Firenze

2. 

Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S. Marta 3, 50139 Firenze

3. 

Universidad de Valladolid, Departamento de Matemática Aplicada, ETSII, Paseo del Cauce s/n, 47011 Valladolid

Published  February 2008

In recent years, the area of nonautonomous dynamical systems has matured into a field with recognizable contours together with well-defined themes and methods. Its development has been strongly stimulated by various problems of applied mathematics, and it has in its turn influenced such areas of applied and pure mathematics as spectral theory, stability theory, bifurcation theory, the theory of bounded/recurrent motions, etc. Much work in this field concerns the asymptotic properties of the solutions of a nonautonomous differential or discrete system. However, that is by no means always the case, and the reader will find papers in this volume which are concerned only at a distance or not at all with asymptotic matters.
   There is a close relation between the field of nonautonomous dynamical systems and that of stochastic dynamical systems. They can be distinguished to a certain extent by the observation that a nonautonomous dynamical system often arises from the study of a differential or discrete system whose coefficients depend on time, but in a non-stochastic way. The limiting case is that of periodic coefficients, but one is also interested in equations whose coefficients exhibit weaker recurrence properties; for example almost periodicity, Birkhoff recurrence, Poisson recurrence, etc. A distinction also occurs on the methodological level in that topological methods tend to find more application in the former field as compared to the latter (while analytical and ergodic tools are heavily used in both). In any case, some people use the term “random dynamics” to refer to both fields in a more or less interchangeable way.

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