These are some problems I've thought about and would like to see solved. Some of them are mine, some I'm just passing on.

- Are the periodic points dense in multidimensional, strongly irreducible SFTs?

I recently showed that there exist aperiodic strongy irreducible subshifts in any dimension >1, which is slightly related (but the problem is open). - Some questions about automorphisms of shifts of finite type.
- A question about genericity and approxiation in the space of connected systems.
- Is there a factor-universal cellular automaton?
- Is there a ratio ergodic theorem (Hopf's theorem) for actions of non-abelian gruops?

Kieran Jarrett proved that one does exist for the Heisenberg groups).

On the other hand I showed that some groups (even some abelian groups) do not admit ratio theorems.

- Some questions about recurrence and entropy in topological systems.

I answered the first problem in this paper

The last problem in the link above was answered for nilpotent groups by Huang, Jin and Ye. - Can the divergence of Gibbs measures at zero temperature be observed at the level of finite marginals?

Solved by Coronel and Rivera-Letelier in this paper (Appendix A) - Can we estimate an eigenvalue(s) of a process by observing finite samples?

Solved (under some regularity conditions) by Anthony Quas. - Is the multidimension odd shift sofic?

Solved in dimension 2 by Julien Cassaigne.

- A survey of open problems rekated to Henon maps (January 2024).
- Some Open Problems in Dynamical Systems & Ergodic Theory from Katsiveli 2000, with occasional updates.
- The Stony Brook problem page.
- Mike Boyle's open problems in symbolic dynamics.
- Nikos Frantzikinakis's survey of open problems on non-conventional ergodic averages.
- Alex Gorodnik's page contains an open problems survey
- Anatole Katok's problem page, and an old survey of his containing open problems (many perhaps closed by now).
- Some problems on algebraic dynamics by Tom Ward.
- Oliver Knill's Open problem's in Hamiltonian dynamics
- Problems from the 3rd Pingree Park workshop.

The first problem in the file was solved by Ville Salo. - Problems from icmds2010 (in video!).

- Itai Benjamini has some problems on his homepage (mostly in probability).
- Michel Talagrand's fiscal stimulus.
- Some problems in probability by David Aldous.

- The big ones from the Clay Institute.