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When harmonic maps from the Riemann sphere into the complex projective space are energy bounded, it contains a subsequence converging to a bubble tree map f I : T I ! CP. We show that their q-transforms and q-transforms are also energy bounded. Hence their subsequences converge to harmonic bubble tree maps f I1 1 : T I1 ! CP and f I 1 1 : T I 1 ! CP respectively. In this paper, we show relations between f I , f I1 1 and f I 1 1 .

Harmonic maps from the Riemann sphere into the complex projective space and the harmonic sequences