Investigation of the dynamical systems on deformed tent map

Studies on dynamical systems appear in many disciplines. Among these works, the map, which is known as tent map in the literature and takes its name from the similarity of its graphic to a tent, has an important place. The dynamics of the tent map is analyzed in a simpler way in the binary system and its periodic points can be written in a general form. Also, the tent family has an interesting dynamic and the bifurcation diagram can be illustrated. In this thesis, firstly, the tent family and bifurcation diagram are given in detail after the classical tent map is expressed in binary. Then, using the construction of the tent map, deformed tent maps are expressed in binary, and a general formula is given for these dynamical systems. In addition, after the periodic points are expressed in a general form for the first version of the deformed tent map, the chaoticity of this dynamical system in the sense of Devaney is investigated. Also, a family is defined for this dynamical system and the bifurcation diagram is given. In the last part of the thesis, a different deformed tent map is discussed using this construction. We also show that whether these tent maps are topologically conjugate or not.