Please use this identifier to cite or link to this item:
http://hdl.handle.net/123456789/833
Title: | Monodromy Groups of Fuchsian Differential Equations |
Authors: | Dhiman, Rishabh |
Keywords: | Mathematics Differential Equations Fuchsian Differential Equations Monodromy Group |
Issue Date: | 15-Jul-2017 |
Publisher: | IISER-M |
Abstract: | In this thesis, we study the monodromy groups of Fuchsian Differential Equa- tions and its properties. We find circuit matrices at all singularities of a Fuchsian differential equation. These circuit matrices forms a group called monodromy group. In a Fuchsian differential equation, if there are three singularities then we can predict the properties of its monodromy group by finding the trace of circuit matrices at all singularities. Chapter 1 deals with basic deffnitions and terminologies. In Chapter 2, we provide a formula to calculate the traces of the circuit matrices at singular points which depends on analytic coefficients of our Fuchsian differential equation. We state our main theorem in Chapter 3 and discuss few examples. In Chapter 4 we prove several interesting group theoretic lemmas that are needed for the main theorem and outline the proof of our main theorem. All our proofs and examples can be found in |
URI: | http://hdl.handle.net/123456789/833 |
Appears in Collections: | MS-12 |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
MS-12082.pdf | 21.54 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.