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I've been reading Lectures on dynamical systems by E. Zehnder. This book is undergraduate text and its intoductory chapter is about ergodic systems (with Birkhoff's theorem proved), which I found interesting.

I would like to know what is the good reference for further reading on ergodic theory (not necessarily an undergraduate text), based on topics that are covered in this book.

(Similar questions were posted, but the most of the proposed books seemed difficult for reading.)

Also, I would like to know more about applications of ergodic theory and does there exist any textbook in ergodic theory?

Any help is welcome. Thanks in advance.

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The absolute classic ergodic theory is An introduction to Ergodic Theory by Peter Walters. It treats the standard topics for a first course in ergodic theory, and includes sevaral applications to other branches of math.

If you are looking for a number theoretical view, there is Ergodic Theory: with a view towards Number Theory by Einsiedler and Ward, which, as the title suggests, presents a lot of applications to number theory, like Furstenberg's proof of Szemeredi's theorem.

My personal favorite is Foundations of Ergodic Theory, by Viana and Oliveira. It is a book full of examples and exercises, as well as applications and excellent explanations. It is also easier to read than the previous ones, and includes appendices on measure theory and functional analysis.

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