With greek polutonic keyboard layout I can type greek characters with diacritics like:
άὰᾶᾳᾷᾴᾲ
but I cannot type combination of those with both dasia signs, i.e.:
ἄἂἆᾆᾄᾂ and
ἅἃἇᾇᾅᾃ.
This is, however, possible in all GTK apps. I observed this on different distros and different computers.

The compose sequence to type ἄ is ";:a" but the result is ά instead of ἄ. I could type this bug report in firefox but could not produce the sign neither in qt assistant etc., nor qupzilla, nor konsole, nor kate etc.