On 1-Manifolds and 2-Manifolds

Abstract

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.