Distribution of Kolmogorov-Sinaï entropy in self-consistent models of barred galaxies (Q1976082)

The authors investigate the models of self-consisted barred galaxies constructed with Schwarzschild method by using the Kolmogorov-Sinaï entropy \(h_{KS}\). The Kolmogorov-Sinaï entropy of an orbit can be determined as the rate at which it looses information about its initial conditions. As was shown by \textit{Ja. B. Pesin} [Usp. Mat. Nauk 32, No. 4 (196), 55-112 (1977; Zbl 0359.58010)], the entropy \(h_{KS}\) is equal to the sum of positive Lyapunov exponents (which show the level of chaos in a model). For a given orbit \(J\), a proper measure of this loss (or gain, depending on the viewpoint) of information is \(h_{KS_J}=\sum_{\lambda_{k_j}>0}^4\lambda_{k_j}\). In Hamiltonian systems the entropy \(h_{{KS}_J}\) vanishes only for regular orbits. Orbits with non-zero \(h_{{KS}_J}\) have a sensitive dependence on initial conditions which can be a possible criterion for the chaos. For the computation of solutions for \(\min(h_{KS})\) and the \(\max(h_{KS})\) models, the authors use the objective function \(h_{KS}=\sum _{j=1}^{N_{orb}}h_{{KS}_j}X_j\), where \(h_{KS}\) is the Kolmogorov-Sinaï entropy of the whole system. The spatial distribution of the Kolmogorov-Synaï entropy (\(h_{{KS}_i}\)) can then be obtained in the form \(h_{{KS}_i}= \frac{1}{M_i}\sum_{j=1}^{N_{orb}} h_{{KS}_j}B_{ij}X_j\), where \(M_{i}\) is the mass inside the cell with number \(i\), \(B_{ij}\) are cells and \(X_j\) is a weight (\(X_j \geq 0\)), for the cell with number \(j\). The authors apply the spatial distribution of Kolmogorov-Sinaï entropy \(h_{KS}\) to the investigation by numerical methods of the morphology of barred galaxies. It is shown that the most models considered contain ``semi-chaotic'' orbits confined inside the corotation. The article contains many figures, diagrams etc.