557/ICOT –
Although it’s certainly an interesting problem as stated, the one problem with describing it as pursuer (X) and pursued (Y) is that it does not factor in reaction time. In order for Y to travel in the perpendicular direction of travel of X for any infinitesimal movement (during your time t_i), Y must know X’s direction of travel before X actually performs said movement. Assuming that this is impossible, X can randomly preempt the direction of travel of Y and cut him off, and after enough guesses should eventually catch him. I’m with ICOT in not understanding your entire logic (I’m an engineer, not a mathematician :)), so please correct me if I’m wrong.