Asymptotic (statistical) periodicity in two-dimensional maps

<p style='text-indent:20px;'>In this paper we give a new sufficient condition for the existence of asymptotic periodicity Frobenius–Perron operators corresponding to two–dimensional maps. Asymptotic strictly expanding systems, that is, all eigenvalues system are greater than one, in high-dimensional dynamical was already known. Our result enables one deal with systems having an eigenvalue smaller one. The key idea proof is use function bounded variation defined by line integration. Finally, introduce two-dimensional numerically exhibiting different periods depending on parameter values, and discuss application our theorem example.</p>