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Article overview
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Unique ergodicity of circle and interval exchange transformations with flips | C. Gutierrez
; S. Lloyd
; V. Medvedev
; B. Pires
; E. Zhuzhoma
; | Date: |
24 Nov 2007 | Abstract: | We study circle exchange transformations on three subintervals, that reverse
orientation on at least one of the subintervals (a ’flip’). We prove that if
such a transformation has exactly one flip, then it has a periodic orbit and
thus no dense orbit. For the cases of two and three flips, we construct
uniquely ergodic minimal examples by finding a periodic point of an adapted
Rauzy--Veech renormalisation operator. Finally, by means of an inductive
reasoning, we show that for any $n geq 4$ and $1 leq f leq n$, there exist
uniquely ergodic transitive circle exchange transformations on $n$ subintervals
with $f$ flips. | Source: | arXiv, 0711.3821 | Services: | Forum | Review | PDF | Favorites |
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