A Study of fractal properties of turbulent functions

Title

A Study of fractal properties of turbulent functions

Creator

Vincent, N S.

Contributor

Kumar, Vinod P B.

Description

The studies have been mainly done in the discrete dynamical systems in topological spaces, we study the various types of relationships between chaotic functions and turbulent functions, a study of turbulent newlinefunctions in metric spaces, and the fractal nature of turbulent functions. In connection with this we study the relationship between turbulent function and chaos, also the relation between fractals and chaos. First newlinepart of the work gives a holistic outlook over the concepts like Turbulent Functions, Chaos and Fractals.Viewing the relevance of studying the irregular sets in the present and future scenario, we started our work newlinefocusing on the fractal nature of turbulent functions. The study incorporates the concepts like turbulent function, chaos and fractals along with rapid fluctuations. According to Robert Devaney, the three ingredients of chaos are sensitivity, density and transitivity. Rapid fluctuations newlineare very much connected with sensitive functions and turbulent functions. We could not and any implied relation between turbulence and sensitive functions. So we study the other two ingredients of chaos, newlinetransitivity and density. 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. Hence we study the fractal properties of turbulent function in a topological view point.The question that we have faced during the discussion and study of fractal properties of turbulent function is that whether a given turbulent function newlinef in a compact metric space provides an attractor and if there is an attractor, will it be a fractal.

Source

Author's Submission

Date

2017-01-01

Publisher

Christ(Deemed to be University)

Subject

Mathematics and Statistics

Rights

Open Access

Relation

61000080

Format

PDF

Language

English

Type

PhD

Identifier

http://hdl.handle.net/10603/204288