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My teacher ask me to start to study about Hamilton systems, Noether theorem. I am not advanced in that kind of study, so the teacher want from me to see some easy research, some proofs, step by step. Let's say, the teacher wants from me to try to understand alone the introduction in Hamiltonian systems.

So, I want to find out information about Infinitesimal transformation. Where can I find this information. How do these transformation help the mathematicians and physicians? Which is the role of these infinitesimal transformation.

Which is easiest way to understand infinitesimal transformation?

These transformation help me to understand Noether Theorem?

What should I know about Infinitesimal transformation?

I have found some information in the following link:

http://www.damtp.cam.ac.uk/user/tong/dynamics/clas.pdf

thanks!

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This book defines infinitesimal point transformations:

Title: An introduction to the Lie theory of one-parameter groups : with applications to the solution of differential equations

Author: Cohen, Abraham

Collection: Historical Math Monographs

Cornell Library

They are defined on page 7, one can read up the first few pages to get acquainted with the notation. For point transformations only, see also

http://www.solitaryroad.com/c282.html

for a quick introduction into the subject.

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