Coordinate convergence conjecture for fixed-point-free polydisc self-maps
Let N≥1N\ge1N≥1 and let F:DN→DNF:\mathbb D^N\to\mathbb D^NF:DN→DN be holomorphic and without fixed points. Write F∘nF^{\circ n}F∘n for the nnn-fold iterate and let πj(z)=zj\pi_j(z)=z_jπj(z)=zj be projection onto th…