caa a22 4500 386377936 CHVBK 20180307112028.0 cr unu---uuuuu 161130e198903 xx s 000 0 eng 10.1017/S0143385700004818 doi S0143385700004818 pii (NATIONALLICENCE)cambridge-10.1017/S0143385700004818 Dufour Jean-Paul Gétodim, Institut de Mathématiques, U.S.T.L., Pl. E. Bataillon, 34000 Montpellier, France Existence de cycles pour des multi-applications du cercle [Elektronische Daten] [Jean-Paul Dufour] We consider multi-applications Γ of the circle S1, the graphs of which are ‘degree (1, 1)', continuous piece-wise monotonic curves of S1 × S1 In general Γp is not a connected curve but it is a union of a degree (1, 1) continuous curve Γp of S1 × S1 and of some other curves homotopic to a point. Using these Γp we are able to study dynamics of Γ. We focus on the case where Γ has no periodic points and we see, for instance, that all ‘regular' orbits have, on S1 the same order as orbits of an irrational rotation. Using this we prove that such F without ‘cycles' are obtained from a Denjoy's counter-example, perturbing it in the holes of the invariant set. Finally we generalize the classical result of Block and Franke showing that if Γ is a C2 curve with no degenerate critical points, or if Γ is a C∞ curve with no ‘flat' points, there are always ‘cycles', unless Γ is an homeomorphism. Copyright © Cambridge University Press 1989 Ergodic Theory and Dynamical Systems Cambridge University Press 9/1(1989-03), 47-65 0143-3857 9:1<47 1989 9 ETS https://doi.org/10.1017/S0143385700004818 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0143385700004818 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dufour Jean-Paul Gétodim, Institut de Mathématiques, U.S.T.L., Pl. E. Bataillon, 34000 Montpellier, France NATIONALLICENCE 773 0- Ergodic Theory and Dynamical Systems Cambridge University Press 9/1(1989-03), 47-65 0143-3857 9:1<47 1989 9 ETS CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge