Diophantine property in the group of affine transformations of the line
We investigate the Diophantine property of a pair of elements in the group of affine transformations of the line. We say tha t a pair of elements 71,72 in this group is Diophantine if there is a number A such tha t a product of length I of elements of the set {71,72, 7f 1 , jf 1 } is either the unit...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2014
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| Sorozat: | Acta scientiarum mathematicarum
80 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| mtmt: | http://dx.doi.org/10.14232/actasm-013-757-6 |
| Online Access: | http://acta.bibl.u-szeged.hu/34837 |
| Tartalmi kivonat: | We investigate the Diophantine property of a pair of elements in the group of affine transformations of the line. We say tha t a pair of elements 71,72 in this group is Diophantine if there is a number A such tha t a product of length I of elements of the set {71,72, 7f 1 , jf 1 } is either the unit element or of distance at least A~l from the unit element. We prove tha t the set of non-Diophantine pairs in a certain one parameter family is of Hausdorff dimension 0. |
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| Terjedelem/Fizikai jellemzők: | 447-458 |
| ISSN: | 0001-6969 |