• Login
    View Item 
    •   Home
    • Massey Documents by Type
    • Theses and Dissertations
    • View Item
    •   Home
    • Massey Documents by Type
    • Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Holomorphic solutions to functional differential equations : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealand

    Icon
    View/Open Full Text
    02_whole.pdf (3.488Mb)
    01_front.pdf (568.4Kb)
    Export to EndNote
    Abstract
    Functional differential equations with an entire functional argument g are examined and theory regarding the presence of holomorphic solutions to these equations presented. There are two main problems analysed, each related to the other. The first is the existence of local holomorphic solutions about a point fixed under g, and the second is the analytic continuation of such a solution throughout the complex plane. The local behaviour of g about its fixed points determines whether holomorphic solutions exist about such points, whilst the global behaviour of g under iteration determines the analytic continuation of these solutions. The dynamics of the functional argument g, therefore, is the driving force in both problems. Both a local and global theory is developed for the existence of solutions, and for defining where such solutions are holomorphic. The case where g is a polynomial is considered in detail, although much of the theory applies equally well to the general case where g is entire.
    Date
    2005
    Author
    Marshall, Jonathan Craig
    Marshall, Jonathan Craig
    Rights
    The Author
    Publisher
    Massey University
    URI
    http://hdl.handle.net/10179/2614
    Collections
    • Theses and Dissertations
    Metadata
    Show full item record

    Copyright © Massey University
    | Contact Us | Feedback | Copyright Take Down Request | Massey University Privacy Statement
    DSpace software copyright © Duraspace
    v5.7-2020.1-beta1
     

     

    Tweets by @Massey_Research
    Information PagesContent PolicyDepositing content to MROCopyright and Access InformationDeposit LicenseDeposit License SummaryTheses FAQFile FormatsDoctoral Thesis Deposit

    Browse

    All of MROCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister

    Statistics

    View Usage Statistics

    Copyright © Massey University
    | Contact Us | Feedback | Copyright Take Down Request | Massey University Privacy Statement
    DSpace software copyright © Duraspace
    v5.7-2020.1-beta1