TY - JOUR ID - 2436 TI - On 1-Manifolds and 2-Manifolds JO - Iranian Journal of Science JA - ISTT LA - en SN - 2731-8095 AU - El-Ghoul, M. AU - El-Abed, A. AD - Permanent Address Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt AD - Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah, KSA Y1 - 2014 PY - 2014 VL - 38 IS - 3.1 SP - 373 EP - 377 KW - Chaotic KW - manifolds KW - folding KW - retraction KW - geodesics DO - 10.22099/ijsts.2014.2436 N2 - 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. UR - https://ijsts.shirazu.ac.ir/article_2436.html L1 - https://ijsts.shirazu.ac.ir/article_2436_bfa2d3bb69ed98bff0b5a8af4c1a24e9.pdf ER -