Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/800
Title: Monodromy Groups of Fuchsian Differential Equations
Authors: Dhiman, Rishabh
Keywords: Mathematics
Differential Equations
Fuchsian Differential Equations
Matrices
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/123456789/800
Appears in Collections:MS-12

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