There is no such thing as a fixed point in space or time.  It's constantly changing.  Even with theortecial reverse time travel, you could end up at a point in your past, and automatically diverge into a new universe simply by being there, even if you lived in a hole the entire time and no one ever saw you...  which in fact isn't a point in the past at all, but a point in your future...  Yay multiverse!