Problem of stability and chaotic properties of multidimensional Lasota equation in the context of Matuszewska-Orlicz indices

We study asymptotic properties of the dynamical system generated by the multidimensional Lasota equation. We give the conditions of its stability and chaos in the sense of Devaney in Orlicz spaces. We apply Matuszewska-Orlicz indices to a description of asymptotic behavior of the considered semigroup. We analyze also the conditions under which asymptotic behavior for more general form of the equation is provided. An example illustrates the criteria when the semigroups generated by the equations have not asymptotic behavior.