Attracting and repelling in homogeneous signal processes

Attracting and repelling are discussed on two levels: in abstract signal processes and in signal processes arising as returns to a fixed set in an ergodic dynamical system. In the first approach, among other things, we give three examples in which the sum of two Poisson (hence neutral—neither attracting nor repelling) processes comes out either neutral or attracting, or repelling, depending on how the two processes depend on each other. The main new result of the second type concerns so-called 'composite events' in the form of a union of all cylinders over blocks belonging to the δ-ball in the Hamming distance around a fixed block. We prove that in a typical ergodic nonperiodic process the majority of such 'composite events' reveal strong attracting. We discuss the practical interpretation of this result