---
tag: VFZRVZ9SD8
kind: concept
name: Minimal period
msc: [37C25, 37B02]
sources:
  - url: https://en.wikipedia.org/wiki/Periodic_point
---

## Summary

The minimal period, or prime period, of a [[periodic point|T75CZ5H47N]] is the least number of steps after which it returns to itself.
It equals the number of distinct points in its orbit.
Every period of the point is a multiple of the minimal period.
Results such as Sharkovskii's theorem are stated in terms of minimal periods.

## Explanations

### L1 human

A periodic point comes back to its start after some steps, and then again and again.
The minimal period is the length of one trip around the loop.
For the rotation of a clock face by $3$ hours, the point at $12$ visits $3$, $6$, $9$ and returns to $12$.
So its minimal period is $4$, even though it is also back after $8$ or $12$ steps.