At the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop on “Recent Progress in Dynamics” in September–October 2004 the speakers and participants were asked to state open problems in their field of research, and much of this problem list resulted from these contributions. Thanks are due, therefore, to the Clay Mathematics Institute and the Mathematical Sciences Research Institute for generously supporting and hosting this workshop, and to the speakers, who graciously responded to the suggestion that open problems be stated whenever possible, and who in many cases kindly corrected or expanded the renditions here of the problems that they had posed. It is my hope that this list will contribute to the impact that the workshop has already had. It was helpful to this endeavor and is a service to the community that most lectures from the workshop can be viewed as streaming video at http://www.msri.org/calendar/workshops/WorkshopInfo/267/show workshop.
In this list, almost all sections are based on an original version written by myself about the problems as presented by the proposer in a talk during the workshop. The proposer is identified by the attribution “(presented by…)” in the section heading. Where the proposer undertook significant modification of this original version, the section became attributed to the proposer (without “presented by”). Section 8 and Section 13 were contributed by their authors without any preliminary draft by myself and were only slightly edited by me, and Section 11 is based in good part on the questions raised by Keith Burns in his talk but was written collaboratively.