Автор |
J S W Lamb |
Автор |
G R W Quispel |
Дата выпуска |
1995-11-01 |
dc.description |
We consider discrete invertible dynamical systems L with the property that the kth iterate L<sup>k</sup> possesses (reversing) symmetries mat are not possessed by L. A map U is called a (reversing) k-symmetry of L if k is the smallest positive integer for which U is a (reversing) symmetry of L<sup>k</sup>. In this paper we discuss the particular case that L possesses a cyclic reversing k-symmetry group. We derive a decomposition property of maps that possess a cyclic reversing k-symmetry group and we classify the occurrence of such groups in invertible dynamical systems. We discuss the occurrence of nonsimultaneously linearizable nonisomorphic reversing k-symmetry groups in maps possessing cyclic reversing k-symmetry groups, illustrated by an example of a diffeomorphism on the plane R<sup>2</sup>. We also construct examples of diffeomorphisms with cyclic reversing k-symmetry groups on the circle S<sup>1</sup>, on the two-torus T<sup>2</sup>, and on the cylinder S<sup>1</sup>*R. |
Формат |
application.pdf |
Издатель |
Institute of Physics Publishing |
Название |
Cyclic reversing k-symmetry groups |
Тип |
paper |
DOI |
10.1088/0951-7715/8/6/007 |
Electronic ISSN |
1361-6544 |
Print ISSN |
0951-7715 |
Журнал |
Nonlinearity |
Том |
8 |
Первая страница |
1005 |
Последняя страница |
1026 |
Аффилиация |
J S W Lamb; Inst. for Theor. Phys., Amsterdam Univ., Netherlands |
Аффилиация |
G R W Quispel; Inst. for Theor. Phys., Amsterdam Univ., Netherlands |
Выпуск |
6 |