Timeline for excplicit formula of iterates of an interval exchange
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Mar 6, 2014 at 15:22 | comment | added | user8991 | i do not understand your question. if $f$ is a rotation of angle $\alpha$, then $f^n(0)=n \alpha$, and i want an analogous formula when $f$ is an interval exchange (or at least, some information of some kind). | |
| Mar 5, 2014 at 14:44 | comment | added | user39115 | I guess, but I am not sure, that by explicit formula you mean a computable function F that depends on f^k(0), for k<m and m is fixed, such that F(n)=f^n(0). I think you need to specify what exactly you want to mean by explicit formula. | |
| S Mar 5, 2014 at 14:43 | history | suggested | CommunityBot | CC BY-SA 3.0 |
added complementary information and question
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| Mar 5, 2014 at 14:38 | review | Suggested edits | |||
| S Mar 5, 2014 at 14:43 | |||||
| Mar 1, 2014 at 11:58 | comment | added | user8991 | is Rauzy-veech induction relevant for this problem? | |
| Mar 1, 2014 at 10:23 | comment | added | user8991 | maybe you are right, replace "it implies" by "it is implied". I am only interested in the case of rational lengths. | |
| Mar 1, 2014 at 1:08 | comment | added | Douglas Zare | Why would the lengths of the intervals have to be rational? The implication in the other direction is obvious, but it seems like you could take a periodic interval exchange map and break it up into one with irrational lengths that is essentially the same. Is that ruled out by the definitions or some other standard assumption? | |
| Feb 28, 2014 at 23:28 | comment | added | user8991 | that there exists $n$ such that for any $x$, $f^n(x)=x$. it implies that the lengths of intervals are rational. | |
| Feb 28, 2014 at 17:34 | comment | added | Anthony Quas | What do you mean $f$ is periodic? that $f^n(x)=x$ for all $x$ for some $n$? | |
| Feb 28, 2014 at 14:04 | comment | added | user8991 | combinat.sagemath.org/doc/reference/combinat/sage/combinat/iet/… | |
| Feb 28, 2014 at 13:57 | comment | added | user8991 | en.wikipedia.org/wiki/Interval_exchange_transformation | |
| Feb 28, 2014 at 13:56 | comment | added | Felix Goldberg | What's an interval exchange transformation? | |
| Feb 28, 2014 at 13:55 | history | asked | user8991 | CC BY-SA 3.0 |