Prof. V. Romanovski with Prof. D. S. Shafer from University of North Carolina, Charlotte, has published a scientific monography with the reputed Birkhaeuser - Springer publishing company. The topics covers the problems of polynomial first order ordinary differential equations in the plane and the questions and problems stated in the celebrated 16th Hilbert problem. Romanovski is one of the worldwide leading authorities in this field of research. The book summarizes the results of the scientific community including the authors' important contributions over the past two decades.
COBISS.SI-ID: 62709761
Series of papers on the theme nonautonomous (time dependent) Hamilton systems, which have been published in the few past years by M. Robnik, V.G. Romanovski, H.-J. Stoeckmann and A. V. Kuzmin, on theme the linear time dependent oscillator, have a natural logical continuation in treatment of nonlinear nonautonomous Hamilton systems, their adiabatic invariants and statistical properties of the energy of a microcanonical ensemble of initial conditions. This research is now intensely continued and the review paper sets some new directions in this future development.
COBISS.SI-ID: 63328513
Several years lasting research has been concluded with a publication of a paper. In the paper we verify the validity of the Brezin-Zee- Hackenbroich-Weidenmueller (BZHW) theory, and in particular we study the speed of the transition from low-dimensional (N=2) to high- dimensional regime. We find that the transition is fast. If one of the BZHW assumptions is not satisfied, we see that the limiting statisistics of the eigenvalues differs from GOE. The paper is one of the first systematic studies of non-Gaussian matrix ensembles, and indicates new research directions.
COBISS.SI-ID: 1618791
The authors present a method for investigating the cyclicity of an elementary focus or center of a polynomial system of differential equations by means of complexification of the system and application of algorithms of computational algebra, showing an approach to treating the case that the Bautin ideal of focus quantities is not a radical ideal. They illustrate the method with a family of cubic systems.
COBISS.SI-ID: 62112257
V. Romanovski published a series of original papers and the research programme group reaches about 2700 SCI citations. (M. Cvetič has 12000.) The important paper of Romanovski with coworkers (J. Gine) is the study of linearizability for Lotka-Volterra planar complex cubic systems. They find the necessary and sufficient conditions for the linearizability and derive the conditions for the isochronicity.
COBISS.SI-ID: 63328769