Search for invariant sets of the generalized tent map

This paper describes a predictive control method to search for unstable periodic orbits of the generalized tent map. The invariant set containing is repelling with complicated Cantor-like structure. Therefore, simple local stabilization orbit may not be enough find orbit, due small measure basin attraction. It shown that certain values parameter, both behavior and global solutions change in controlled system; particular, enlarges become an interval or entire real axis. computational particularities using system are considered, necessary conditions given. question asymptotic stability subcycles system's stable cycles fully investigated, some statistical properties subset classical Cantor middle thirds determined by points map described.