Exploration of Fractal Dimensions and Measure of Chaos in a Cubic Map

Fractal Dimensions and appearance of chaos play very crucial role in studying the dynamical behavior of a nonlinear system, particularly a cubic map in the form () = + 2 + 3 , where , are well-defined parameters .In this paper, we develop some methods to calculate fractal dimensions for our proposed cubic map.We mainly evaluate Box-Counting (Grid-Counting) dimension, Information Dimension, Correlation and Generalized Dimension in the cubic map , and a meta analysis is carried out on the role of chaos in such a map .A few open problems are highlighted