Abstract: The studies have been mainly done in the discrete dynamical systems in topological spaces. According to Robert Devaney, the three ingredients of chaos are sensitivity, density and transitivity. We answer a series of questions like whether the iterated function system can be chaotic. Will the contractions are Devaney chaotic. If we can find such a chaotic contraction, will it generate a self similar set? If there is such a self similar set, will it be a fractal? In order to answer the question, we have gone for generalization with continuous maps and homeomorphisms.
Keywords: Devaney Chaos, Fractals, Fractal Dimension, Self Similarity, Sensitivity, Topological Transitivity.
Title: Generalizations in Fractals
Author: Vincent N. S.
International Journal of Interdisciplinary Research and Innovations
ISSN 2348-1218 (print), ISSN 2348-1226 (online)
Research Publish Journals
