Images of birds in Taviani´s Kaos and Ghost dog

In the same week i saw Ghost Dog i watched Kaos by the Taviani brothers. Birds are an important item in both films. For the Taviani brothers the film Kaos begins with the capturing of a crow. The crow is released but released and it gets a bell around his neck. Every story begins with the crow and his bell on beautiful music.
In Ghost Dog primal communication between Gost Dog and Loui is done by a pigeon. Almost all the pigeons have been killed at the end of the movie but the one which is very important survives, even survives Ghost dog. I am still thinking how important the birds are in both movies. Perhaps Jarmush was inspired by the Italian brothers?? I am curious about the influence. Does one Jarmush freak knows more?