The Bifurcations of Completely Integrable Holonomic Systems of First-Order Differential Equations

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review of the article axioms–2787231

Bifurcations of completely integrable holonomic systems of first-order differential equations

Jingbo Xu, Kangping Liu, Xiaoliang Cheng

 

In the work, the authors consider a first-order holonomic differential equation with a complete integral for one real function. A classification of bifurcations of such differential equations is presented. Analysis of the work leads to the following observations:

 

1. Mathematical symbolism should be excluded from the annotation text.

2. In section 1, emphasize the relevance and novelty of the research.

3. Section 3 is not appropriate as presented; the formulation of Theorem 2 should be combined with the proof.

4. There is no section for discussing the results, indicating the application of the result obtained.

5. There is no conclusion section.

 

Conclusion. For publication, these comments must be corrected.

 

Reviewer.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Report on the paper

Bifurcations of completely integrable holonomic systems of first-order differential equations

by Jingbo Xu, Kangping Liu, Xiaoliang Cheng

 

The aim of the authors is to 'investigate the classification of bifurcations of completely integrable holonomic first-order differential equation germs which satisfy that the corresponding one-parameter integral diagrams are $R^+$-simple and stable'.

The paper has theoretically valuable content, and is based on basic results of S. Izumiya and M. Takahashi.

Some large formulas are well handled in formating them. But not all the cases in the main result, Theorem 2, are proved. 

In fact I think a short comment for each case, or similar cases, have to be done, in order to give the reader a good reason to cover all the cases.

A section containing concluding remarks would be wellcame, pointing out more ideas, or to comment the classification.

I recommend the publication after fulfilling the above.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Review of the article axioms 2787231
Bifurcations of completely integrable holonomic systems of first
order differential equations
Jingbo Xu, Kangping Liu, Xiaoliang Cheng

The authors took into account the comments from the first round in the revised version of the article.
Conclusion. The revised version of the article can be recommended for publication

Reviewer

Comments for author File: Comments.pdf