### Article

## Современное изложение классификации грубых преобразований окружности

Mathematician A.G. Mayer from Nizhny Novgorod was the first who classify rough diffeomorphisms on a circle. This was one of the pioneering works on the topological classification of dynamic systems. However, the classification results in the work of A.G. Mayer obviously did not stand out, they were part of the proof of the roughness and genericity of Morse-Smale diffeomorphisms on a circle, and the realization problem was not solved. In the present work, the authors, as successors of the Nizhny Novgorod school of nonlinear oscillations, present a solution to the problem of the topological classification of rough transformations of a circle in a canonical formulation using modern methods and approaches. Namely, in the first theorem the type of periodic data of rough transformations of the circle is established, in the second theorem there are necessary and sufficient conditions for their conjugation, in the third theorem an admissible set of parameters is realized by a rough transformation of the circle