Talk:Torus breakdown

From Scholarpedia
Jump to: navigation, search

    Reviewer A (who resigned later)

    (comments moved from the main text by the editor-in-chief)

    I browsed the article quoted below. It obviously appears that the authors did not treat the problem in its generality (Torus breakdown) is a very wide topic and only focuss their article on their own work. Among the topics which should be mentionned :

    Curry-Yorke scenario Ruelle-Takens scenario Baptista & Caldas scenario

    among others...

    Going into details right now is useless (I believe) since the article does not reach its target...

    AUTHOR REPLY: Probably it is some kind of misunderstanding. The subject of the article is only "torus breakdownn", and not all scenaria related to the onset to chaos where the torus plays a role. For example, the Ruelle-Takens scenario mentioned by the reviewer deals with the appearance of a strange attractor on the torus: the torus still exists after the bifurcation; this is a subject different from the one described in the article.

    reviewer C

    I think the introductory section could be more self-a bit more explanatory for those who are not already experts; in particular f_epsilon is said to be a dynamical system but no mention is made of phase space, or indeed that the torus will correspond to an invariant curve for a mapping. These things may seem trivial to the expert but I think they are important to those trying to learn about the subject from this resource.

    reviewer D

    The theory of torus breakdown was originally developed by V. S. Afraimovich and L. P. Shilnikov . Hence, there are obviously no substantial points of criticism. However, there are a number of more formal points that requires attention:

    (i) there should be a reference to work on higher order tori, including to the Takens' conjecture.

    (ii) it may be useful to clarify the distribution between loss of smoothness in discrete points on the resonance torus and the actual process of torus breakdown

    (iii) it may also be useful to clarify the distinction between torus breakdown in smooth and in non-smooth systems.

    (iv) the use of definite (the) and indefinite (a) articles is inconsistent with the meaning of the article. Corrections should be made throughout the text.

    (v) spelling: line 20 write: period-doubling, reference 8 write: Rayleigh.

    (vi) Figure: Does B1 intersect B+ as indicated? We miss an illustration of the destructed torus outside of the resonance tonque.

    (vii) See Also: "Bubbling Transition" appears not to be directly related to the present subject.

    Personal tools

    Focal areas