Research Projects

Complex dynamics, a field that originated from Newton's method of finding the roots of complex analytic functions, has been a subject of study since the early 20th century. It deals with the behavior of an iteration sequence and extends the dynamics of one complex function to the dynamics of a compose of two or more such functions. This leads to a rich study of semigroups of complex functions, which are generated by a sequence of transcendental entire functions. The researchers aim to investigate topological aspects of the Julia set and escaping set of a transcendental semigroup, as well as the topological properties of the Bungee set of an entire function. They also aim to study the dynamics of the semigroup of quasiregular maps and investigate wandering domains in quasiregular dynamics. The proposed problems are emerging areas in complex dynamics, and there is a vast scope of research to be carried out. The researchers hope to provide partial answers to some of the proposed problems, as the field is still open and there is much to be explored.