4 problems

Multiple recurrence conjecture. If $z\in P$ is ML-random, then there exists $n$ such that

Let $f_c$ be an infinitely renormalizable real quadratic polynomial, and let $J_{f_c}$ denote its Julia set. Computability is understood relative to an oracle for the parameter $c$…

Computable invariant measure conjecture. Every computable dynamical system should have a computable invariant measure.

A computable dynamical system is a dynamical system whose underlying space and dynamics admit the relevant finite algorithmic descriptions, and an SRB measure is a Sinai–Ruelle–Bow…