There are hardware converters that will convert HDMI to various other types of Video signals, however there are some issues doing so that you should be aware of.
In order to convert HDMI signal, it is highly recommended the converter be HDCP compliant. If you attempt to use a non-compliant converter, it will not allow you to watch HDCP protected content such as that from the iTunes Store or other protected video content.
Some users who have attempted to convert to DVI for their TV's without HDMI have gotten the connection to work using a DVI-to-HDMI cable. The only concern would be that DVI does not carry audio, so alternative connections would need to be explored to push audio out from the Apple TV. DVI doesn't necessarily support HDCP as well as other standards used by HDMI (which may or may not be an issue depending on your specific devices)
If you wish to view any HDCP content on your Apple TV you will not be able to use it in conjunction with our analog converters. Because of the HDCP content issues it will not support a converter that does not support HDCP. None of our HDMI to analog converters fully support HDCP, so they will not work for the Apple TV. Unfortunately this is an issue with the Apple TV and Apple will not have any adapters or updates that would allow you to get around this issue.