1

Could you recommend a differential equations textbook that has a section that defines the monodromy of a differential equation with worked examples? Undergraduate or beginner graduate is fine -- the main thing is for the book to have definitions and worked examples of the monodromy group.

EDIT: I should be more clear, since I think this reference request hasn't been asked before. Given a differential equation, I want a book that explains to me how to compute its monodromy.

The problem is, either the differential equations book doesn't have anything about monodromy, or the book is about monodromy from the point of view of algebraic geometry with sheaves, fibered products, etc etc and not just about a simple differential equation.

Camilo
  • 175

1 Answers1

4

You can try the book

E. Hille, Ordinary differential equations in the complex domain.

It has a section 5.7 (with exercises in the end) on monodromy.

For more challenging reading:

Y. Ilyashenko, S. Yakovenko, Lectures on Analytic Differential Equations. Chapter III deals with monodromy.

Or you can try

D.Anosov, A.Bolibruch, The Riemann-Hilbert Problem.

The book works out many examples but is not a textbook.

Lastly:

H.Zoladek, The Monodromy Group.

(I am not suggesting Deligne's book.)

Moishe Kohan
  • 97,719
  • Did you look at things like Galois Theory of Linear Differential Equations – reuns Jul 19 '19 at 06:09
  • @reuns: I did not know about the book. I looked at the most relevant section; it is a nice book for a professional mathematician, however, I think it will be too hard for a beginner. (But so are the last two books on my list.) I think, Hille's book is the best intro (for a beginner interested in the ODE side) in that I know. – Moishe Kohan Jul 19 '19 at 07:54
  • Yup, looks like a good graduated series of books that fits what I was looking for. Thanks, I'll go ahead and accept, this question isn't particularly lively :). – Camilo Jul 20 '19 at 07:18