Timeline for Zero entropy and the Koopman representation
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2021 at 21:16 | vote | accept | Vladimir | ||
| Nov 3, 2021 at 20:16 | answer | added | R W | timeline score: 3 | |
| Nov 3, 2021 at 16:26 | comment | added | Vladimir | Indeed, if you consider just the zero-mean subspace then ergodicity is equivalent to having no invariant vectors. And yes: I am asking which properties of the representation imply or are implied by zero entropy. | |
| Nov 3, 2021 at 15:25 | comment | added | ARG | I would think you can tell, since for any set $A$ you can realise in $\mathsf{L}^2$ by its characteristic function $1_A$. But you might be asking which property of the Koopman representation imply (or are implied by) zero entropy? An example in this vein: ergodicity (if my memory serves me well) is equivalent to the coefficients of the representation to have zero mean. [As a side note: I think you need to restrict $\mathsf{L}^2$ to functions whose integral w.r.t. $\mu$ is 0. Otherwise you get lots of fixed vectors for the representation: the constant functions] | |
| Nov 3, 2021 at 14:12 | history | asked | Vladimir | CC BY-SA 4.0 |