Open Problems

The Furstenburg Conjecture and Rigidity
If two commuting endomorphisms of a torus are incommensurable (no power of one is a power of the other), then their joint action should be rigid. Some of the conjectures and open problems compiled by the AIM.
http://aimath.org/WWN/furstenburg/

Open Problems in Dynamical Systems
A collection of papers outlining unsolved problems maintained at Stony Brook.
http://www.math.sunysb.edu/dynamics/open.html

Open Problems in Dynamical Systems and Ergodic Theory
Originally from the Katsiveli 2000 Open Problems Session, now maintained by Sergiy Kolyada. PDF/PS.
http://www.math.iupui.edu/~mmisiure/open/