Problem 134

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1. If $\varphi _t$ is flow on a homogeneous space $G/ \Gamma$ with positive entropy, then there exists a compact $\varphi _t$ invariant section for the action of $N$
2. If the flow has entropy 0 and is ergodic, does this mean that there is  no $N$?

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FL

(For part 1.) Hardly legible. Wild guess here. Don't see what that means.

FL

(part 2) Is $\varphi _t$ a one parameter subgroup here? and $N$ associated to it?