Intuition and visualization of area preserving maps?

by BAYMAX   Last Updated August 24, 2018 10:20 AM

I was trying to understand what is meant by "area preserving map"?. I was going through the Wolfram article about the area preserving map here but any motivation, intuition or visualization to understand the area-preserving maps, like how it is connected with the determinant being $\pm 1$?, would not it be helpful if we could visualize the area-preserving maps?.

I don't think this soft question about the motivation about the area-preserving maps has been asked before, also will be helpful if one could help with references?. Also, I find it in many research articles.

I could find the following questions on MSE-

*) Non-examples of area preserving map .

*)example of area preserving twist maps

*)area-preserving iff |det|=+1

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