The Structure of Disjoint Groups of Continuous Functions
Let I be an open interval. We describe the general structure of groups of continuous self functions on I which are disjoint, that is, the graphs of any two distinct elements of them do not intersect. Initially the class of all disjoint groups of continuous functions is divided in three subclasses: c...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/790758 |
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| author | Hojjat Farzadfard B. Khani Robati |
| author_facet | Hojjat Farzadfard B. Khani Robati |
| author_sort | Hojjat Farzadfard |
| collection | DOAJ |
| description | Let I be an open interval. We describe the general structure of groups of continuous self functions on I which are disjoint, that is, the graphs of any two distinct elements of them do not intersect. Initially the class of all disjoint groups of continuous functions is divided in three subclasses: cyclic groups, groups the limit points of their orbits are Cantor-like sets, and finally those the limit points of their orbits are the whole interval I. We will show that (1) each group of the second type is conjugate, via a specific homeomorphism, to a piecewise linear group of the same type; (2) each group of the third type is a subgroup of a continuous disjoint iteration group. We conclude the Zdun's result on the structure of disjoint iteration groups of continuous functions as special case of our results. |
| format | Article |
| id | doaj-art-26b7b6bdab304bb88fcb556e594ac062 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-26b7b6bdab304bb88fcb556e594ac0622025-02-03T06:48:05ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/790758790758The Structure of Disjoint Groups of Continuous FunctionsHojjat Farzadfard0B. Khani Robati1Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71457-44776, IranDepartment of Mathematics, College of Sciences, Shiraz University, Shiraz 71457-44776, IranLet I be an open interval. We describe the general structure of groups of continuous self functions on I which are disjoint, that is, the graphs of any two distinct elements of them do not intersect. Initially the class of all disjoint groups of continuous functions is divided in three subclasses: cyclic groups, groups the limit points of their orbits are Cantor-like sets, and finally those the limit points of their orbits are the whole interval I. We will show that (1) each group of the second type is conjugate, via a specific homeomorphism, to a piecewise linear group of the same type; (2) each group of the third type is a subgroup of a continuous disjoint iteration group. We conclude the Zdun's result on the structure of disjoint iteration groups of continuous functions as special case of our results.http://dx.doi.org/10.1155/2012/790758 |
| spellingShingle | Hojjat Farzadfard B. Khani Robati The Structure of Disjoint Groups of Continuous Functions Abstract and Applied Analysis |
| title | The Structure of Disjoint Groups of Continuous Functions |
| title_full | The Structure of Disjoint Groups of Continuous Functions |
| title_fullStr | The Structure of Disjoint Groups of Continuous Functions |
| title_full_unstemmed | The Structure of Disjoint Groups of Continuous Functions |
| title_short | The Structure of Disjoint Groups of Continuous Functions |
| title_sort | structure of disjoint groups of continuous functions |
| url | http://dx.doi.org/10.1155/2012/790758 |
| work_keys_str_mv | AT hojjatfarzadfard thestructureofdisjointgroupsofcontinuousfunctions AT bkhanirobati thestructureofdisjointgroupsofcontinuousfunctions AT hojjatfarzadfard structureofdisjointgroupsofcontinuousfunctions AT bkhanirobati structureofdisjointgroupsofcontinuousfunctions |