О сопряженности перекладываний двух открытых интервалов окружности без периодических точек
We classify up to conjugacy the subgroups of certain types in the full, in the affine, and in the special affine Cremona groups. We prove that the normalizers of these subgroups are algebraic. As an application, we obtain new results in the Linearization Problem generalizing to disconnected groups Bialynicki-Birula's results of 1966-67. We prove ``fusion theorems'' for n-dimensional tori in the affine and in the special affine Cremona groups of rank n. In the final section we introduce and discuss the notions of Jordan decomposition and torsion prime numbers for the Cremona groups.
It is shown that the main result of N. R. Wallach, Principal orbit type theorems for reductive algebraic group actions and the Kempf–Ness Theorem, arXiv:1811.07195v1 (17 Nov 2018), is a special case of a more general statement, which can be deduced, using a short argument, from the classical Richardson and Luna theorems.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.