Le Calvez, Patrice Existence d’orbites quasi-périodiques dans les attracteurs de Birkhoff. (Existence of quasiperiodic orbits in Birkhoff attractors). (French) Zbl 0602.58031 Commun. Math. Phys. 106, 383-394 (1986). For each number \(\rho\) between the lower and the upper rotation number of the Birkhoff attractor of a dissipative monotone twist map, there is a periodic or quasiperiodic orbit with rotation number \(\rho\). Cited in 17 Documents MSC: 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 37G99 Local and nonlocal bifurcation theory for dynamical systems Keywords:lower and upper rotation number; periodic orbit; quasiperiodic orbit; Birkhoff attractor PDFBibTeX XMLCite \textit{P. Le Calvez}, Commun. Math. Phys. 106, 383--394 (1986; Zbl 0602.58031) Full Text: DOI References: [1] Birkhoff, G.D.: Sur quelques courbes fermées remarquables. Bull. Soc. Math. Fr.60, 1-26 (1932); aussi dans Collected Math. Papers of G. D. Birkhoff, Vol. II, p. 418-443, New York: Dover 1968 · Zbl 0005.22002 [2] Birkhoff, G.D.: Sur l’existence de régions d’instabilité en dynamique, Ann. Inst. Henri Poincaré8 (1932) et Collected Math. Papers, Vol. II, p. 444-461 [3] Charpentier, M.: Sur quelques propriétés des courbes de M. Birkhoff. Bull. Soc. Math. Fr.62, 193-224 (1934) · Zbl 0010.37701 [4] Chenciner, A.: Séminaire Bourbaki, n{\(\deg\)} 622. Astérisque,121-122, Soc. Math. de France 147-170 (1985) [5] Hall, G.R. A topological version of a theorem of Mather on twist maps. Ergodic Theory Dyn. Syst.4, 585-603 (1984) · Zbl 0564.58019 [6] Herman, M.: Sur les courbes invariantes par les difféomorphismes de l’anneau. Astérisque103-104, Soc. Math. de France (1983) [7] Katok, A.: Some remarks on Birkhoff and Mather twist map theorem. Ergodic Theory Dyn. Syst. 185-192 (1982) · Zbl 0521.58048 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.