On a structure of the space wandering orbits of diffeomorphisms on surfaces with the finite hyperbolic chain recurrent set

In the present paper a class $\Phi$ of diffeomorphisms on surfaces $M^2$ with the finite hyperbolic chain recurrent set is considered. To each periodic orbit $\mathcal O_i,~i=1,\dots,k_f$ of $f\in\Phi$ corresponds a representation of the dynamics of a diffeomorphism $f$ in the form “source — sink”, where source (sink) is a repeller $R_i$ (an attractor $A_i$) of diffeomorphism $f$. It is assigned that the orbit space of the wandering set $V_i=M^2\setminus(A_i\cup R_i)$ is a collection of the finite number of two-dimention torus. It implies, in particular, that the restriction of $f$ to $V_i$ is topologically conjugated with the homothety.