Dynamical Systems and Their Applications
Dynamical systems theory, being one of the rapidly developing areas of modern mathematics, provides powerful theoretical base for exploring a variety of models that arise in natural and social sciences, engineering and technology. The combination of the internal wealth and beauty of results with the exceptional practical importance motivates a growing number of specialists to study into dynamical systems.
Research carried out in Ukraine plays an important role in the development of dynamical systems theory. Back in the late XIX century, A. M. Lyapunov laid the foundations of the modern theory of stability. In the 30-40s of XX century, the fundamental contribution to the theory of dynamical systems with invariant measure and to statistical mechanics was made by N. N. Bogolyubov and ensuing investigations in this direction have led in the second half of XX century to the creation of stochastic dynamical system theory, including methods for studying the asymptotic behavior of multiparticle systems in random media. During the same time, ukrainian mathematicians have also deployed extensive research in the topological dynamics of one- and low-dimensional dynamical systems, as well as in infinite-dimensional dynamical systems generated by continuous time difference equations and boundary value problems of mathematical physics; the results obtained in these areas has long been recognized in the world.
Beginning with the 60s, the Institute of Mathematics held conferences and schools on various fields of mathematics, in particular, on dynamical systems. This has had a profound effect on the development not only of dynamical systems theory but also of the overall nonlinear dynamics. Not so long, the Institute of Mathematics decided to arrange International Conference “Dynamical Systems and Their Applications” (ICDSA), aimed to promote transnational cooperation and share good practice in the field of dynamical systems theory. The first conference hosted in Kyiv in 2012. The second edition of ICDSA will be held again in Kyiv, it will consider a wide range of issues of the modern theory of dynamical systems, among which are topological dynamics, ergodic theory, the theory of attractors and chaos, combinatorial and symbolic dynamics, the theory of fractals, bifurcation and stability theory, infinite-dimensional dynamical systems, and various kinds of applications, especially in mathematical physics. Emphasis is expected to be paid to combinatorial dynamics, originating from the widely known theorem on the coexistence of cycles, published in “Ukrainian Mathematical Journal” for 1964. In 1994 the International conference “Thirty Years after Sharkovskii's Theorem: New Perspectives” (Spain) was devoted to advances and new problems in combinatorial dynamics, and in 2014 combinatorial dynamics can celebrate its 50th anniversary.