Problem 134

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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 $N$
If the flow has entropy 0 and is ergodic, does this mean that there is no $N$ ?

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Entropy

Homog

Ergodic

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FL

Permalink Submitted by Ledrappier on Mon, 11/14/2016 - 17:51

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

FL

Permalink Submitted by Ledrappier on Mon, 11/14/2016 - 17:52

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

$jathreya's picture$

In the setting where $G = SL

Permalink Submitted by jathreya on Tue, 08/01/2017 - 12:27

In the setting where $G = SL(2, \mathbb R)$ , Yitwah Cheung and I built a section to the horocycle flow for $\Gamma = SL(2, \mathbb Z)$ , and with Jon Chaika and Samuel Lelievre built one for $\Gamma = \Delta(2, 5, \infty)$ . This construction was generalized by Uyanik-Work, and Sarig-Schmoll showed how to realize the horocycle flow as a suspension flow over an adic transformation.

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FL

FL

In the setting where $G = SL

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