Lyapunov’s direct method in estimates of topological entropy

An upper estimate for the topological entropy of a dynamical system defined by a system of ODE is obtained. The estimate involves the Lyapunov functions and Losinskii’s logarithmic norm. The proof uses the known fact that the topological entropy of a mapping acting in a compact space K can be estimated via the fractal dimension of K. Bibliography: 28 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 62–75. Translated by V. A. Boichenko and G. A. Leonov.