## Dynamics of an inequality

The dynamics D∋(ri,ri+1)↦(ri+1,ri+2)∈D on the set D:={(x,y)∈R2:x>0,y>x2/2} is given by the recurrence ri+2=r2i+12+1r3i+1(ri+1−r2i2) for i=0,1,…. Questions: Is it true that the only periodic sequence (ri) here is the constant one with ri=1 for all i? Take any natural n. Suppose that the sequence (ri) is periodic with period n and r0⋯rn−1=1. Does it then always … Read more