Timeline for The topological entropy of potential space filling curves on the unit interval
Current License: CC BY-SA 4.0
8 events
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| Jul 15 at 15:26 | comment | added | Anthony Quas | OK. I understand the question now. I thought you were asking about the richness of the collection of all space-filling curves. But it now sounds as though you are talking about the dynamical properties (the first coordinate of) one space filling curve. | |
| Jul 14 at 8:54 | comment | added | Ali Taghavi | @AnthonyQuas is injectivity of f the point you are indicating to?or you meqn consideration of a precise example of $f$? | |
| Jul 14 at 8:47 | comment | added | Ali Taghavi | @AnthonyQuas I think topologicql entropy is defined for non injective maps too. Here $f$ is a map on the interval which is composition of the projection $\pi_2$ with a space filling curve. so we have a dynamic on the interval | |
| Jul 14 at 2:14 | comment | added | Anthony Quas | I guess my comment is that I only know how to define entropy when there is a dynamical system. In your question, you have a space, but I don’t see the dynamics. | |
| Jul 13 at 10:18 | comment | added | Ali Taghavi | @AnthonyQuas Thank you for your comment. In fact by this post I am curious about the diversity of space filling curve from the entropy point of view. What quantities can be realized as the entropy of some potential filling curve? Can one say that the entropy is always non zero? | |
| Jul 13 at 0:48 | comment | added | Anthony Quas | Is there a map that you are considering applying? | |
| Jul 12 at 21:48 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jul 12 at 21:36 | history | asked | Ali Taghavi | CC BY-SA 4.0 |