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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Orbit structure of interval exchange transformations with flip

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Nogueira, Arnaldo [1] ; Pires, Benito [2] ; Troubetzkoy, Serge [3]
Total Authors: 3
[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
Document type: Journal article
Source: Nonlinearity; v. 26, n. 2, p. 525-537, FEB 2013.
Web of Science Citations: 7

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: 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems
Grantee:Jorge Manuel Sotomayor Tello
Support type: Research Projects - Thematic Grants
FAPESP's process: 09/02380-0 - Flows on surfaces and exchange transformations
Grantee:Benito Frazao Pires
Support type: Research Grants - Young Investigators Grants