In this work, different types of chaotic 1-manifolds which lie on the chaotic spheres or on a torus are introduced.
Some types of retractions of the chaotic spheres affect on the 1-chaotic systems, and other types of retractions
occur to the geometric manifold but make the 1-chaotic manifold invariant. The existed retractions are discussed
through new proved theorems. Also we construct different types of folding of 1-chaotic manifolds which are
homeomorphic to S1and their indicatrixes.
)