Aster's Stalker

Our cat, Aster, has a stalker. There is a neighborhood cat, who we call black and white cat ('cus he is black and white, duh) that mostly lives next door. For the past few days he has been walking up the stairs to our apartment and hopping up on a short wall near one of our windows. He then sits there, looking into the apartment and driving our cat crazy. He has also started leaning over to the window and pawing at the screen. I keep chasing him away and he keeps coming back. He is a real punk about it too. I have to pick him up, he hisses at me, I set him down, give him a scoot in the rear, he will go halfway down the stairs, stop, I give him another scoot and he parks it at the bottom of the staircase. Brat. He is a big cat and probably pretty tough since he lives outside and all, but Aster would whoop the crap out of him if she got out. I am thinking of taping a picture of a snarling dog to the window to scare him. That won't work though.