Do hybrid mobile apps support Push Notifications?

I work at AppMobi. We do provide push notifications for iOS and Android out of the box. It's simple to enable and we have a javascript helper library to manage setup/processing/showing in your code. We have a web service API to send messages to, or you can use our Dashboard to send them.

PhoneGap on Android supports push notifications by adding a plugin. See here. I'm not sure about other platforms. appMobi supports out of the box push notifications for Android and iOS. See here. I can find some vague references for Titanium, but nothing specific.

Trigger.io supports creating hybrid apps with push notifications using only web technologies - no need to setup for local compiles or use Eclipse / XCode.

Our documentation for including push notifications is here: http://docs.trigger.io/en/v1.3/partners/parse.html

We've also blogged a tutorial here: http://trigger.io/cross-platform-application-development-blog/2012/03/23/using-parse-and-trigger-io-for-cross-platform-apps-without-pain-in-the-back-end/