INVARIANTS OF PERIOD TYPE FOR ONE-DIMENSIONAL DYNAMIC SYSTEMS

The problem about co-existence of the periodical, almost periodical and recurrent orbits of the one-dimensional dynamic systems has been investigated. The case of the systems generated by a continuous representation of n-od into itself has been considered. In it for recurrent points of the dynamic systems the invariant (utrafilter on natural numbers) which is the analog of the periodical point period has been determined, its properties and connection with D-function playing role of the period for almost periodical points hava been studied. The generalization of the Sharkovski theorem for recurrent points of the continuos representations of n-od into itself has been obtained. Namely, for continuous representation of n-od into itself the complete desrciption of the possible sets for periods of the periodical points and D-functions of the almost periodical and recurrent points has been given. The investigation of the multiplicity of the periods and D-functions for stability in the space of the continuous representations of n-od with topological even convergence has been performedAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio