The dynamics of the family λsec (z)
Other Title(s)
ديناميكية العائلة λsec (z)
Dissertant
Thesis advisor
University
University of Baghdad
Faculty
College of Science
Department
Mathematics Department
University Country
Iraq
Degree
Master
Degree Date
2008
English Abstract
The dynamics of the family of meromorphic maps fλ(z) =λ tan(z) has been studied by Devaney and keen[15], while Kapoor and Prasad [21] described the dynamical behavior of the entire transcendental non-critically finite function fλ(z) = λ(ez-1) / z ; λ > 0.
In addition, Devaney [13] described some of the bifurcations that occur in the family of entire maps fλ(z) = λ exp(z) ,when λ=1.
In the present thesis the dynamics of the one parameter family Ƭ = {fλ(z) = λ sec(z) for z , λ R} is studied.
It is found that there exist three parameter values λi = Φ(xi) ,(i = 1,2,3), where Φ(x) = and x1, x3 are the real roots of Φ′ (x) = 0 while x2 is the solution of x + cot x = 0.
The nature of the fixed points of the family Ƭ1 = {fλ(x) = λsec(x),x R, λ R} is discussed.
The bifurcation points of the family are found.
Finally the Julia set of the function fλ(z) are investigated analytically as well as numerically.
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Main Subjects
Topics
No. of Pages
101
Table of Contents
Table of contents.
Abstract.
Abstract in Arabic.
Introduction.
Chapter One : Julia sets.
Chapter Two : Dynamics of the family λsec (z).
References.
American Psychological Association (APA)
al-Husayni, Hasan Fadil Rida. (2008). The dynamics of the family λsec (z). (Master's theses Theses and Dissertations Master). University of Baghdad, Iraq
https://search.emarefa.net/detail/BIM-602008
Modern Language Association (MLA)
al-Husayni, Hasan Fadil Rida. The dynamics of the family λsec (z). (Master's theses Theses and Dissertations Master). University of Baghdad. (2008).
https://search.emarefa.net/detail/BIM-602008
American Medical Association (AMA)
al-Husayni, Hasan Fadil Rida. (2008). The dynamics of the family λsec (z). (Master's theses Theses and Dissertations Master). University of Baghdad, Iraq
https://search.emarefa.net/detail/BIM-602008
Language
English
Data Type
Arab Theses
Record ID
BIM-602008
