An approach to the analysis of risks in a dynamic formulation is considered. A system of generalized relationships describing the dynamics of the human-engineering object-environment system and qualitative analysis using a generalized description of dynamic systems making use of the potential risk surfaces are utilized. The system dynamics is characterized by attractors in the phase (or configuration) space, and the attractor stability specifies the constancy of the system safety. The topology of the potential surface (principal curvatures, relative distribution of characteristic points) determines the stability and the dynamic behavior of the system as well as the possibility of transition from one attractor to another. This makes it possible to evaluate the probability of emergency situations or catastrophes by analyzing a chain of transitions from one attractor (system state) to another.