The transition from finite to infinite measures in dynamical systems
Dynamics of transformations coupled with interval exchange transformations
| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Aix Marseille Univ 163, Inst Math Luminy, F-13288 Marseille 9 - France
[2] Univ Sao Paulo, Dept Comp & Matemat, BR-14040901 Ribeirao Preto, SP - Brazil
[3] Aix Marseille Univ, Inst Math Luminy, Ctr Phys Theor, Federat Rech Unites Math Marseille, F-13288 Marseille 9 - France
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Nonlinearity; v. 26, n. 2, p. 525-537, FEB 2013. |
| Web of Science Citations: | 7 |
| Abstract | |
A sharp bound on the number of invariant components of an interval exchange transformation (IET) is provided. More precisely, it is proved that the number of periodic components n(per) and the number of minimal components n(min) of an interval exchange transformation of n intervals satisfy n(per) + 2n(min) <= n. Moreover, it is shown that almost all IETs are typical, that is, all have stable periodic components and all the minimal components are robust (i.e. persistent under almost all small perturbations). Finally, we find all the possible values for the integer vector (n(per), n(min)) for all typical IET of n intervals. (AU) | |
| FAPESP's process: | 09/02380-0 - Flows on surfaces and exchange transformations |
| Grantee: | Benito Frazao Pires |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| FAPESP's process: | 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems |
| Grantee: | Jorge Manuel Sotomayor Tello |
| Support Opportunities: | Research Projects - Thematic Grants |