Dynamics of Iterative Schemes for Quadratic Polynomial

摘要

Most of the fractals are generated by applying a map recursively to an initial point or a set of the space such as complex plane. An orbit of a point is a sequence of iteratively obtained points from it and the orbit is said to be diverging when its points grow unbounded. A set of all the points whose orbits are not diverging may be termed as a fractal. The fractal dynamics of the orbits depends on the rule of iteration also. In this paper, we study the dynamics of iterations for a number of iterative schemes. The results regarding the escape criteria for quadratic complex polynomials under various iteration procedures are established.