# Talk:Equivariant dynamical systems

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.

Marty

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