cookie name with dot cannot be saved?

I didn't see this issue has been reported before, but it really happend with my following code:

if(isset($_COOKIE[$this->cookieName])&&$_COOKIE[$this->cookieName]==true)
{
return false;
}
else
{
return true;
}
it always return true with a name which include dot, like 123.txt_abcedef.
When I use the name without dot, it works fine.
It costs me about a day to find it out.