Talk:Hamiltonian normal forms

I edited the paper a bit, removing { and } in the references, and one typo. Article is fine, maybe going too much into detail in the end. Does one need permission from Springer to publish the figures here? JS

Editor: Yes, the author needs to secure the permission or change the figures.

Remarks by Reviewer A:

It might be good to define "involution" the first time you use it.

Your discussion of H-bar and H_2 as integrals is confusing because you have not mentioned the change of coordinates. The original H is expressed in one set of coordinates, the new H-bar is expressed in another. Then H-bar and H_2 are exact integrals for H-bar, but they are not approximate integrals for H until you truncate H-bar and then express both of them in the old variables.

Also you say that they are approximate integrals for H, "so" they are exact integrals for H-bar. This "so" does not make sense. The inference actually goes the other way.

It is important to get the first few paragraphs very clear, because they make it possible for a reader to go on. The rest of the article is a summary of more advanced results and is not expected to be completely clear, but the basics should be.

In the first line about the 1:2 resonance you say "have have".

The rest of the article is ok with me.

Remarks by Reviewer C:

I've done a bit of editing of the article Mostly to clarify--at least I think the new version is clearer.

I don't really understand what symmetry is imposed for the 3 d.o.f. case. I suppose it must be a reflection in the q_1 and q_2 axes? In any case, it would be nice to be more explicit.

Otherwise, though the article does not really explain how to construct normal forms, it gives a nice overview of results and open problems.