I see that there are apps that will broadcast certain things to an Apple TV via AirPlay, but is there a way to send a view of the screen in real time via this method? I have seen iPhone 4S doing this, but the only apps I've seen for Android advertise that they broadcast media files as if they're being sent as opposed to streamed.
I don't know of any apps that can do that, but (supposedly) any Android 4.2 device can do that with a wireless display adapter connected to an HDMI-enabled TV. I also found this project by E.S.R.Labs, which they successfully get a Nexus S to mirror it's screen (albeit onto a Raspberry Pi). Mirroring functionality is also sometimes limited due to hardware requirements.
I also recently found that a developer was able to get Miracast working on Nexus 7 and 4 variants. Check it out on XDA with videos. Something cool to note with this project is that the mirroring capabilities are all software based; no need for additional hardware. Hopefully that will also lead to further development for mirroring on devices that don't already have the hardware inside of them.