Collatz conjecture
Choose a positive whole number. Halve it if it is even; otherwise triple it and add one. Repeat. Does every starting number reach one?
Dynamics
Repeated maps, billiard trajectories and periodic motion.
Subjects: Analysis and dynamics
Problems in this collection
5 problemsFurstenberg’s ×2, ×3 conjecture
Must an atomless circle distribution preserved by doubling and tripling be uniform?
Birkhoff billiard conjecture
Are ellipses the only smooth strictly convex planar billiards that are integrable near the boundary?
Dynamical uniform boundedness conjecture
Can finite arithmetic orbits be bounded by map degree and number-field degree alone?
Hilbert’s sixteenth problem: limit cycles
A polynomial rule for motion in the plane can create isolated repeating trajectories. How many can occur when the polynomial degree is fixed?