caa a22 4500 477037003 CHVBK 20180405111308.0 cr unu---uuuuu 170330e19960501xx s 000 0 eng 10.1007/BF02439310 doi (NATIONALLICENCE)springer-10.1007/BF02439310 Heteroclinic cycles in bifurcation problems with O (3) symmetry and the spherical Bénard problem [Elektronische Daten] [P. Chossat, F. Guyard] Summary: It has been known since a paper of Armbruster and Chossat ([AC91]) that robust heteroclinic cycles between equilibria can bifurcate in differential systems which are invariant under the action of the groupO(3) defined as the sum of its "natural” irreducible representations of degrees 1 and 2 (i.e., of dimensions 3 and 5). Moreover, these cycles can be seen numerically in the simulation of the amplitude equations resulting from a center manifold reduction of the Bénard problem in a nonrotating spherical shell with suitable aspect ratio ([FH86]). In the present work we first generalize the results of [AC91] to the interactions of irreducible representations of degrees ℓ and ℓ+1 for any ℓ>0. Heteroclinic cycles of various types are shown to exist under certain "generic” conditions and are classified. We show in particular that these conditions are satisfied in most cases when the differential system proceeds from a ℓ, ℓ+1 mode interaction bifurcation in the spherical Bénard problem. Springer-Verlag New York Inc., 1996 Chossat P. I.N.L.N. (CNRS and Université de Nice), 1361, route des Lucioles, 06560, Sophia Antipolis, France aut Guyard F. W.I.A.S., 39, Mohrenstrasse, 10117, Berlin, Germany aut Journal of Nonlinear Science Springer-Verlag 6/3(1996-05-01), 201-238 0938-8974 6:3<201 1996 6 332 https://doi.org/10.1007/BF02439310 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02439310 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chossat P. I.N.L.N. (CNRS and Université de Nice), 1361, route des Lucioles, 06560, Sophia Antipolis, France aut NATIONALLICENCE 700 1- Guyard F. W.I.A.S., 39, Mohrenstrasse, 10117, Berlin, Germany aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 6/3(1996-05-01), 201-238 0938-8974 6:3<201 1996 6 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer