Alexei Zhirov

This paper is a continuation of our previous work where we investigated the class $\mathbb G(M^2)$ of $A$-diffeomorphisms of closed orientable connected surfaces such that their nonwandering sets consist of one-dimensional basic sets (attractors and repellers). In that work, we showed that the dynamical properties of each diffeomorphism from a given class define a collection consisting of nonempty multisets of natural numbers (each such collection contains at least two multisets). These multisets are topological invariants of the diffeomorphism and uniquely determine the topology of the ambient surface. In this paper, we solve the problem of realization of diffeomorphisms from the class $\mathbb G(M^2)$ with respect to a given collection of multisets of natural numbers. We describe all possible collections of multisets from which one can construct a diffeomorphism from the class $\mathbb G(M^2)$, presenting a step-by-step algorithm of construction.