Stable and Unstable Horocycle Flows of the Unit Tangent Bunble $\mathrm{T^1}\mathbb{H}$ of $\mathbb{H}$

Question

Ergodic Theory with a view towards Number Theory, Chapter 9, Page 287, 288.

Let $$\mathbb{H}=\{x+iy \in \mathbb{C}, y>0\}$$ and $\mathrm{T^1}\mathbb{H}$ be the unit tangent bundle of $\mathbb{H}$.

I would like to enquire whether Stable Horocycle Flows (Unstable Horocycle Flows) is the Positive (Negative) Horocycle Flows or the Negative (Positive) one.