Renormalization group and functional self-similarity in various fields of physics

Difference between physical principles of renormalization group transformations in the systems with the infinitely great number of degree of freedom and functional self-similarity of simple physical systems is discussed. Transformations of functional self-similarity in a general form are introduced. The relation between functional and usual self-similary is established. Coincidence between a complex construction of the Kadanoff-type, lying in the basis of a renormgroup of the critical phenomenon theory, and the more obvious property of symmetry leading to functional self-similarity of simple dynamical systems