Bouthaina, GuenezKhouloud, Redjeb2021-12-132021-12-132021http//localhost:8080/jspui/handle/123456789/901The objective of this thesis is to study the dynamical behaviors of the Zeraoulia- Sprott mapping. In particular, this map is the first simple rational map whose fraction has no vanishing denominator and gives chaotic attractors .  In the first chapter, we mentioned some important and comprehensive concepts of dynamical system theory.  In the second chapter, we introduced a two-dimentional smooth discrete bounded map capable of generating multi-fold strange attractors .  In the third chapter we studied periodic 2-orbits of the Zeraoulia-Sprott mapping and we investigete also the bounded and unbounded orbits. Resuméendynamical behaviors/ Zeraoulia- Sprott mapping: rational map: multi-fold strange attractors:Thesis