LINES OF CATASTROPHE: PROBLEMS, EXAMPLES OF SOLUTIONS, CONNECTIONS WITH NEVANLINNA THEORY AND GAMMA-LINES

We introduce a concept of lines of catastrophe which determine those sets where a given vector field or complex function, particularly a solution of a system of equations, has a "bad" behavior. These lines are studied for new wide classes of generalized analytic functions. The obtained results are in some extend similar to the deficiency relation in Nevanlinna theory and in the theory of Γ-lines.