Redirects for Ember app on shared hosting (hostgator)

I have an ember app that I have been building. It has several routes including index (/) and authorization (/authorization). My trouble is that when the application is hosted on hostgator, loading the url http://ift.tt/1KUaGqX results in a 404. This makes sense since there is nothing at that actual url. I need hostgator to redirect all non-file-specific urls to my index.html file.

An example in psuedo code:

if url has extension (.jpg, .pdf, etc)
    serve requested url
else
    serve index.html but retain url in the address bar

I've done this sort of thing with local instances of node when using AngularJs with ui-router, but this is my first time using History-API based routing served from HostGator.

Any suggestions on where to start to set this up?