Dynamics of certain one-parameter and two-parameter families of transcendental functions

Abstract

In the Ph.D thesis, we investigated the dynamics of some one-parameter and two-parameter family of transcendental functions.In Chapter 2, for b 1, the dynamics of function in the two-parameter family , { ( ) z z for : , 0} b f z b b z   F          is investigated. On the real line  , the existence and nature of the fixed points are described. The dynamical behaviour of , f  is exhibited on the real line. The dynamics of , f  on the extended complex, is studied by tracking forward orbits of the singular values of , f  whenever real attracting and rationally indifferent fixed points exist.In Chapter 3, for b 1, the two-parameter family , { ( ) z z for : 0} b g z b b z   G         is considered. On the real line, fixed points and dynamics of , g  is investigated. The dynamics on the complex plane is obtained by tracking the forward orbits of the singular values of , g  . It is shown that a bifurcation occurs in the two-parameter family , g  . Some applications of the dynamics of , g  are provided.