On 1-Manifolds and 2-Manifolds

Document Type: Regular Paper


1 Permanent Address Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

2 Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah, KSA


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.