Applied Physics and Mathematics Annotation << Back NONSMOOTH MAPPINGS. STATIONARY MODELS AND PROBLEMS OF NONSMOOTH DYNAMICS AND ELECTRODYNAMICS. PART 2 A.V. KUKUSHKIN I propose an adequate terminology for operations with multivalued algebraic functions on the complex plane (not on a Riemann surface) with deleted branch points, where the derivative of the function has a pole. For the complex plane with this property, I suggest the name «Riemann plane». It is shown that the special properties of the «Riemann plane» permit to create the theory of non-smooth coordinate transformations on the real plane based on conformal mappings. In this way, the fundamentals of constructing curvilinear coordinate systems with non-smooth coordinate lines are being formulated. Such systems are being shown to be able to mirror image unknown properties of known physical phenomena from dynamics and electrodynamics. In particular, for non-smooth problems in electrodynamics there is an eff ect that can be described as a local violation of the solenoidal nature of the magnetic fi eld. Key words: non-smooth mappings, catastrophe theory, problems of non-smooth dynamics and electrodynamics, coordinate lines with points of nonsmoothness, «Riemann plane» (not on a surface), singular saddle point fi eld, a local violation of the solenoidal nature of the magnetic fi eld Contacts: E-mail: avkuku @gmail.com Pp. 41-56.