I have recently been interested in going deeper into ergodic theory, beyond an introductory level of knowledge. Background wise, my training has mostly been in stochastic analysis, and I have a cursory knowledge of general dynamical systems and ergodic theory, say at the level of the book by Brin and Stuck for general dynamics, and Ward for ergodic theory.

I am especially interested in those aspects of ergodic theory that intersect stochastic analysis, especially stochastic control and filtering. Some examples of papers that deal with this intersection that I have found interesting are Disjointness in Ergodic Theory by Furstenberg and Ergodicity, Decisions, and Partial Information by van Handel.

However, I would also be interested in more general aspects of ergodic theory, though I do not know enough about the field right now to list particular subareas of interest.

Thus my question is twofold :

1. What landmark papers would you recommend to read for someone to get their feet wet in the field? I am especially interested in those with links to stochastic analysis, but if there are more general papers that you think would be important to read, please don’t hesitate to list them!

2. What are the current main research directions in ergodic theory? I would really appreciate a short list, together with a brief description of the subfield.

Thanks in advance!

I have recently been interested in going deeper into ergodic theory, beyond an introductory level of knowledge. Background wise, my training has mostly been in stochastic analysis, and I have a cursory knowledge of general dynamical systems and ergodic theory, say at the level of the book by Brin and Stuck for general dynamics, and Ward for ergodic theory.

I am particularly interested in those aspects of ergodic theory that intersect stochastic analysis, especially stochastic control and filtering. Some examples of papers that deal with this intersection that I have found interesting are Disjointness in Ergodic Theory by Furstenberg and Ergodicity, Decisions, and Partial Information by van Handel.

However, I would also be interested in more general aspects of ergodic theory, though I do not know enough about the field right now to list particular subareas of interest.

Thus my question is twofold :

1. What landmark papers would you recommend to read for someone to get their feet wet in the field? I am especially interested in those with links to stochastic analysis, but if there are more general papers that you think would be important to read, please don’t hesitate to list them!

2. What are the current main research directions in ergodic theory? I would really appreciate a short list, together with a brief description of the subfield.

Thanks in advance!