symmetry of an ordinary differential equation

Let $f:{ℝ}^n\to {ℝ}^n$ be a smooth function and let

$$\dot{x}=f(x)$$

be a system of ordinary differential equations, in addition let $\gamma$ be an invertible matrix. Then $\gamma$ is a  of the ordinary differential equation if

$$f(\gamma x)=\gamma f(x).$$

Example:

• Natural symmetry of the Lorenz equation is a example of a symmetry of a differential equation.