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My goal is to study some kind of nonlinear systems through differential geometry. I did an intensive meeting with my supervisor in which he tried to give me an introduction and a link between the following topics:

  • Points
  • Topology
  • Manifolds
  • Charts (coordinates)
  • Differential manifolds

Finally how to arrive from all this to Lie Brackets.

I followed during the meeting but you immediately understand that in 1 hour and a half you can't get all the details of the concepts we touched during the meeting. For this reason I would like to know if you can suggest me some books/slides/videos or whatever to get more understanding of these concepts.

I am going throught the book : Nonlinear control systems by A.Isidori.

Someone on this forum suggested to look into the work of John M.Lee: Introduction to topological Manifolds, Introduction to Smooth manifolds

I found out, reading the Isidori's book that it lacks a bit of graphical explanations which, in this context, I find really useful.

Can you help me?

Thanks a lot for the help.

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1 Answer 1

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For the first part I used: An introduction to manifolds - Loring W. Tu I like it a lot, in my opinion is a very good book with a lot of nice exercises.

For the Riemannian geometry I used the following notes

http://www.maths.tcd.ie/~dwilkins/Courses/425/RiemGeom.pdf

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