Reversible 2D flow

˙ 𝑥 = 𝑓 (𝑥, 𝑦) ˙ 𝑦 = 𝑔 (𝑥, 𝑦)

is reversible iff it is invariant under the transformation $𝑡 \to - 𝑡$ , $𝑦 \to - 𝑦$ , #m/def/dynamics/flow i.e.

- 𝑓 (𝑥, 𝑦) = 𝑓 (𝑥, - 𝑦) 𝑔 (𝑥, 𝑦) = 𝑔 (𝑥, - 𝑦)

which is to say $𝑓$ is odd w.r.t $𝑦$ and $𝑔$ is even.

Properties

#state/develop | #lang/en | #SemBr