Please use this identifier to cite or link to this item:
Title: A Study of Fractal Properties of Turbulent Functions
Researcher: Vincent, N S.
Guide(s): Kumar, Vinod P B.
Keywords: Density,
Devaney Chaos,
Fractal Demension,
Hausdorff Dimension,
Hausdorff Measure,
Homoclinic Points,
Rapid Fluctuation,
Self Similarity ,
University: CHRIST University
Completed Date: 16/06/2017
Abstract: 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.
Pagination: A4
Appears in Departments:Department of Mathematics and Statistics

Files in This Item:
File Description SizeFormat 
01_title.pdfAttached File90.46 kBAdobe PDFView/Open
02_certificate.pdf966.63 kBAdobe PDFView/Open
03_abstract.pdf101.83 kBAdobe PDFView/Open
04_declaration.pdf57.93 kBAdobe PDFView/Open
05_acknowledgement.pdf63.92 kBAdobe PDFView/Open
06_contents.pdf60.88 kBAdobe PDFView/Open
07_list_of_figures.pdf94.88 kBAdobe PDFView/Open
08_chapter1.pdf652 kBAdobe PDFView/Open
09_chapter2.pdf322.98 kBAdobe PDFView/Open
10_chapter3.pdf215.43 kBAdobe PDFView/Open
11_chapter4.pdf199.84 kBAdobe PDFView/Open
13_chapter6.pdf247.94 kBAdobe PDFView/Open
14_chapter7.pdf259.64 kBAdobe PDFView/Open
15_bibliography.pdf135.92 kBAdobe PDFView/Open
16_appendices.pdf148.63 kBAdobe PDFView/Open

Items in Shodhganga are protected by copyright, with all rights reserved, unless otherwise indicated.