How can I get back at my nasty neighbor?

I live in a duplex, I live on the bottom adn my neighbor lives in the upper complex. He is a total blister. He is a mid thirty year old man with a dog and he is a unsocial prick. Any movement that we happen to mak eor noises from our surround sound, he just throws a tantrum back to where its totally immature. Now he has been throwing our lawn chairs in our yard and ripping up my garden. But i dont have proof of him doing it, but how can I catch him?