caa a22 4500 475796888 CHVBK 20180406123727.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1007/PL00001507 doi (NATIONALLICENCE)springer-10.1007/PL00001507 Determining the self-rotation number following a Naimark—Sacker bifurcation in the periodically forced Taylor—Couette flow [Elektronische Daten] [J. M. Lopez, F. Marques] Abstract.: Systems which admit waves via Hopf bifurcations and even systems that do not undergo a Hopf bifurcation but which support weakly damped waves may, when parametrically excited, respond quasiperiodically. The bifurcations are from a limit cycle (the time-periodic basic flow) to a torus, i.e. Naimark—Sacker bifurcations. Floquet analysis detects such bifurcations, but does not unambiguously determine the second frequency following such a bifurcation. Here we present a technique to unambiguously determine the frequencies of such quasiperiodic flows using only results from Floquet theory and the uniqueness of the self-rotation number (the generalization of the rotation number for continuous systems). The robustness of the technique is illustrated in a parametrically excited Taylor—Couette flow, even in cases where the bifurcating solutions are subject to catastrophic jumps in their spatial/temporal structure. Birkhäuser Verlag, Basel,, 2000 Key words. Floquet theory, self-rotation number, parametric excitation, quasiperiodic flow, Taylor--Couette flow nationallicence Lopez J. M. Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA, US aut Marques F. Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado s/n, Mòdul B4 Campus Nord, 08034, Barcelona, Spain, ES aut https://doi.org/10.1007/PL00001507 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00001507 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lopez J. M. Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA, US aut NATIONALLICENCE 700 1- Marques F. Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado s/n, Mòdul B4 Campus Nord, 08034, Barcelona, Spain, ES aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer