Announcement of Report: A. V. Makarenko, An approach to the symbolic description of dynamical processes defined on continuous time
The report A. V. Makarenko, An approach to the symbolic description of dynamical processes defined on continuous time (\(\mathrm{dom}\,\mathbf{s}(t)=\mathrm{T}\subseteq\mathbb{R}\)), devoted to the synthesis of a finite alphabet for the direct (non-Poincare transformations) describe the shape (geometry of the structure) of the trajectory \(\mathbf{s}(t)\) in \(\mathrm{S}\times\mathrm{T}\) space.
This report presents the preliminary results of of forming the alphabet \(\mathcal{T}\), its basic properties, and the main features in the analysis of the structural properties of dynamic processes and systems that are defined in continuous time. We have written and studied the matrix allowed transitions between characters alphabet \(\mathcal{T}\). For the matrix we obtained an estimate of topological entropy. We have identified a potentially constructive way of symbolic analysis based on the alphabet \(\mathcal{T}\) to analyze the structural properties of the flows. This includes the study of the global structure of trajectories in \(\mathrm{S}\times\mathrm{T}\) space.
Report accepted for International Conference on Differential Equations and Dynamical Systems, June'29 to July'4, 2012, Suzdal, Russia. The sections: "Dynamical Systems". The conference is held under the auspices of: Steklov Mathematical Institute of Russian Academy of Sciences, Vladimir State University and Lomonosov Moscow State University. Read more: www.diff2012.ru.
22 May 2012.
News Source: Own information.
