Splitters are absolutely no use whatsoever, you need a switch.
DVI
Some users with DVI have managed to get their TV's to work with DVI-HDMI cables. DVI carries no audio, so alternative connections need to be explored to enable audio. DVI doesn't necessarily support HDCP as well as other standards used by HDMI (which may or may not be an issue)
Analogue (component, composite etc)
There are hardware converters that will convert HDMI to various other types of output, however there are some issues with doing so that you should be aware of.
HDCP
HDCP compliant converters will not allow you to watch HDCP protected content such as that from the iTunes Store. Non compliant converters exist but we cannot discuss them under the Terms of Use for these communities.
Resolution and aspect ratio
I'm not aware of any converters that will scale the output from the Apple TV, any TV or projector which is used will ideally need to be widescreen and support resolutions of 720p (Apple TV 2), 720p/1080p (Apple TV 3), although the Apple TV does have a number of 4:3 resolutions it supports, but these may not be available if the TV doesn't broadcast them.
DAC
Most types of HDMI to non HDMI connectors or converters won’t carry audio, in such cases you may also need to convert your optical output to an analogue signal using a DAC.
DAC (Example Only - Not a recommendation or suggestion that this is suitable in your circumstances)
