Reference for Ergodic Theory

I am looking for a good introductory book on ergodic theory. Can someone recommend some introductory texts on that?

Solution 1:

You could also try

Ergodic theory with a view towards number theory be Einsiedler and Ward.

Direct link to the online edition

The book is available on springerlink. I do have to warn you that the book can be experienced as quite chaotic but the good thing is that the writers are experts on the topic.

Solution 2:

I recommend Silva, "Invitation to Ergodic theory". This is a wonderful little book. He starts from the ground up, assuming no background except for some competence in analysis, and reaches what seem to be important issues in the theory (I am not an expert). Along the way your knowledge of measure theory should be solidified. For the total novice, the introduction to measure theory, Lebesgue measurable sets, etc., is the best I've seen.

Solution 3:

You can try:

• Paul Halmos – Introduction to ergodic theory

• Harry Furstenberg - Recurrence in ergodic theory and combinatorial number theory

• Dynamical systems and ergodic theory – Mark Pollicott, Michiko Yuri.

The last two are developed to be able to prove some combinatorial results such as van der Waerden's theorem and Szemeredi's theorem.