Talk:Equivariant dynamical systems

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    Jeff, Edgar ---

    The article looks very good. I wonder whether pointing to a few specific applications in fluid dynamics and/or biology might be worth doing. Your call and choice.

    I made a number of small changes --- which I hope will be acceptable. One larger change that I didn't make is to pose differential equations on R^n rather than on a manifold with a comment that this can be generalized. Then I would introduce the vector field notation in example 4. Reason --- the equivariance condition becomes more complicated with manifolds --- and I wonder whether anyone who could understand the manifold notation wouldn't already know what an equivariant system was. Again your call.


    I agree with reviewer A, the article reads very well and could be strengthen with the addition of a few applications that readers unfamiliar with the theory can relate to. In particular, some applications from coupled oscillators could be of great benefit for engineers or related disciplines.

    heteroclinic cycles section

    I originally thought this section was too brief to have value -- there appeared to be no references and no examples. Of course, this is not right. I thought this because I didn't click on the highlighted 'heteroclinic cycles' keyword, which took me to the section with the details. Perhaps there is a way to explicity refer to this section in the way that you refere to the equivariant dynamical systems section in your equivariant bifurcation theory section.

    Marko Budisic: Equivariance on non-euclidean spaces

    Dear authors,

    would it be possible to elaborate a bit more on equivariance condition on non-Euclidean spaces? Specifically, how does one go about constructing the action \(\hat{\gamma}\)? I realize that it might be beyond the scope of this article to treat this question in its full breadth; however, a special case where the dynamics (esp. for maps) evolves on an n-torus is, I believe, sufficiently present in dynamical system to be of interest to readers.

    Best regards, Marko Budisic

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