Skip to main content

Examples of Simply and Multiply Connected Fatou Sets for a Class of Meromorphic Functions | Chapter 04 | Advances in Mathematics and Computer Science Vol. 1

Aims: We give some families of functions which are meromorphic outside a compact countable set B of essential singularities. Our aim is to give some examples of the stable set (called the Fatou set) and the unstable set (called the Julia set) since there are not many examples of parametric family of this class of functions (called in the introduction functions of class K) in complex dynamics.

Study design: We study components of the Fatou set and some theorems related with the iteration of functions in class K and design a computational program to give examples of the Julia and Fatou sets.

Place and Duration of Study: Facultad de Ciencias F__sico Matem_aticas, Benem_erita Universidad Aut_onoma de Puebla, M_exico between June 2011 and July 2012.

Methodology: We use some theorems of complex dynamics in order to study components of the Fatou set. We program some algorithms in C and get some _gures of the Fatou set.

Results: Given a family of functions in class K we get some mathematical results of the Fatou and Julia sets and its _gures for some parameters given.

Conclusion: Taking some families in class K ∩ Sk we give examples of the Fatou set which can be either simply-connected or multiply-connected in the last case the Julia set is a totally disconnected set.

Author  Details:

P. Domínguez
F.C. Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio, Col. San Manuel, C.U., Puebla Pue., 72570, México.

A. Hernández
F.C. Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio, Col. San Manuel, C.U., Puebla Pue., 72570, México.

Read full article: http://bp.bookpi.org/index.php/bpi/catalog/view/46/222/382-1
View Volume: https://doi.org/10.9734/bpi/amacs/v1
Labels:

Comments

Post a Comment

Popular posts from this blog

Greening Regional Airports: A Vision for Carbon Neutral Infrastructure | Chapter 12 | Contemporary Perspective on Science, Technology and Research Vol. 3

 This study provides an overview of the energy demand of a regional airport, divided into individual time horizons. The electrification of aircraft systems raises the question of whether airports will be among the largest electricity consumers in our infrastructure in the future. Sustainability and especially emission reductions are significant challenges for airports that are currently being addressed. The Clean Sky 2 project GENESIS addresses the environmental sustainability of hybrid-electric 50-passenger aircraft systems in a life cycle perspective to support the development of a technology roadmap for the transition to sustainable and competitive electric aircraft systems. This article originates from the GENESIS research and describes various options for ground power supply at a regional airport. Potential solutions for airport infrastructure with a short (2030), medium (2040), and long (2050) time horizon are proposed. In addition to the environmental and conservation benefi...
Post a Comment
Read more

There is No Standard Model of ZFC and ZFC2 | Chapter 03 | Advances in Mathematics and Computer Science Vol. 1

In this Chapter we obtain a contradictions in formal set theories under assumption that these theories have omega-models or nonstandard model with standard part. An possible generalization of Lob’s theorem is considered. Main results are: (i) ¬Con(ZF C+ ∃ M ZFC st ), (ii) ¬Con(N F+ ∃ M NF st ), (iii) ¬Con(ZF C 2 ), (iv) let k be an inaccessible cardinal then ¬Con(ZF C+ ∃ κ), (v) ¬Con(ZF C+ (V=L)), (vi) ¬Con(ZF+ (V=L)). Author   Details: Jaykov Foukzon Israel Institute of Technology, Haifa, Israel Men'kova Elena Romanovna All-Russian Research Institute for Optical and Physical Measurements, Moscow, Russia Read full article: http://bp.bookpi.org/index.php/bpi/catalog/view/46/221/408-1 View Volume: https://doi.org/10.9734/bpi/amacs/v1
Post a Comment
Read more

Study on Processing Method Influences the Effect of Cassava (Manihot esculenta) Consumption on Blood Lipid Profile in Rats | Chapter 8 | Current Research and Development in Chemistry Vol.1

Cassava is consumed in many tropical countries and is fast becoming the major raw material of many diets, especially in the bakery, brewery and pharmaceutical industries. In a study to determine the effects of various formulations of Cassava feeds on blood lipid profile in rats. Forty adult Wistar rats weighing between 120 and 150 g were divided into 4 groups of 10 rats each. The rats were acclimatized for one week; fed with different formulations of Cassava feeds adlibitum, after which the rats were allotted into groups. Group 1 was fed on Garri; group 2 on Cassava flour; group 3 on Tapioca, and the control group (group 4) on normal chow. After 4 weeks, each animal was anaesthetized by exposure to chloroform vapour and blood samples collected by cardiac puncture. Group 1 diet (Garri) significantly increased HDL-cholesterol (HDL-C) concentration and significantly decreased LDL-cholesterol (LDL-C) concentration (p<0.05) compared with the control group. In Group 2 (Cassava flour), t...
Post a Comment
Read more