Applied Physics and Mathematics Annotation << Back NONSMOOTH MAPPINGS. STATIONARY MODELS AND PROBLEMS OF NONSMOOTH DYNAMICS AND ELECTRODYNAMICS. PART 1 A.V. KUKUSHKIN Fundamentals of the theory of non-smooth mappings in a plane with a certain curvilinear coordinate system are being presented. The method employed is the method of conformal mappings in the equivalent complex plane. The mapping is done with an n-sheeted algebraic analytic function, the argument of which is an exponential function defi ned in n sheets of its Riemann surface. The derivative of an algebraic function is being shown to have poles in branch points, where the value of the function itself is fi nite; thus, the mapping is shown to be non-smooth. In this way, the fundamentals of constructing curvilinear coordinate systems with non-smooth coordinate lines are being formulated. For managing and support of the mathematical theory the corresponding dynamics problem for a material point has been formulated and solved. Key words: nonsmooth mappings, catastrophe theory, problems of non-smooth dynamics and electrodynamics, coordinate lines with points of nonsmoothness. Contacts: E-mail: avkuku @gmail.com Pp. 094-118.