Invariant

Definition · applies to quantities, properties, and sets

High school

An invariant is a quantity that stays the same while something else changes.

Undergraduate

An invariant is a quantity or property that does not change under a given transformation or along solutions of a given system.

Examples

Examples

• Energy $H = \frac{1}{2}(p^2 + q^2)$, for the oscillator $\dot{q} = p$, $\dot{p} = -q$ Undergraduate
  The energy $H$ is an invariant, because it is constant along each solution.

Notes

An invariant set of a dynamical system is preserved as a whole, even though its individual points move. See types of set invariance.

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