Tag · 2 problems · 2 fields

Open problems tagged dynamics

2 problems in the Math Lab index touch dynamics, spanning Number Theory, Dynamics & Analysis. Each carries a precise statement, an honest status, and a computational line of attack.

Collatz conjectureNumber Theorylive lab

Halve n if even, map n to 3n + 1 if odd, repeat. The conjecture: every positive integer eventually reaches 1.

a.k.a. 3n + 1 problem · Syracuse problem · hailstone problem · Ulam's conjecture

Outer billiards unboundednessDynamics & Analysisuntouched

For which convex shapes does the outer (dual) billiard map admit unbounded orbits? Moser asked whether orbits can escape to infinity at all.