Stability conditions for nonlinear dynamical systems with a monotonic measure on the phase flow (Q2880006)

The problem of the attraction of trajectories of a dynamical system to equilibrium is considered under almost all initial conditions. The measure of the phase space has the property of monotonicity in the flow, used to examine the attracting set of a dynamical system. Sufficient conditions for the attraction of solutions are found without the assumption of positivity of the divergence of the density function. This result extends the Rantzer approach to the case of abstract dynamical systems in a metric space. The model system of nonlinear differential equations is studied in an explicit form by constructing the density function. The main difficulty in this approach is to construct a Lyapunov measure satisfying the conditions found.