10.18453/rosdok_id00005833 Hui, Ju Hyon Ju Hyon Hui University of Rostock, Institute of Mathematics 2006 510 Mathematics 2006 en https://purl.uni-rostock.de/rosdok/id00005833 urn:nbn:de:gbv:28-rosdok_id00005833-1 In this paper we study criteria of chaos for discrete dynamical Systems governed by noninvertible maps and apply them to the anti-control of chaos. We get some criteria of chaos for discrete dynamical systems governed by noninvertible maps using the subshift in the space of one-side symbolic sequences, and discuss the structural stability of chaotic invariant subsets on a Riemann manifold, and generic chaos. And using these criteria of chaos, we get more generalized conditions to design a controller for the anti-control of chaos.