Addendum to: “Dynamics around the double resonance”

In the end of Section 5 of the paper “Dynamics around the double resonance” [C.-Q. Cheng, Cambridge J. Mathematics, 5(2) (2017) 153–228], we added the sentence the conjecture of Arnold diffusion for positive definite Hamiltonian turns out be a theorem for $n=3$, in page 219, during the proofreading, without the knowledge of the referee or the editors.

Since the referee thinks the statement needs to be justified, we shall show how it is proved in a forthcoming publication.

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Received 15 October 2017

Published 8 January 2018