caa a22 4500 386382654 CHVBK 20180307112048.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500024173 doi S0308210500024173 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500024173 Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry [Elektronische Daten] In this paper we show that in O(2) symmetric systems, structurally stable, asymptoticallystable, heteroclinic cycles can be found which connect periodic solutions with steady states and periodic solutions with periodic solutions. These cycles are found in the third-order truncated normal forms of specific codimension two steady-state/Hopf and Hopf/Hopf mode interactions. We find these cycles using group-theoretic techniques; in particular, we look for certainpatterns in the lattice of isotropy subgroups. Once the pattern has been identified, the heteroclinic cycle can be constructed by decomposing the vector field on fixed-point subspaces into phase/amplitude equations (it is here that we use the assumption of normal form). The final proof of existence (and stability) relies on explicit calculations showing that certain eigenvalue restrictions can be satisfied. Copyright © Royal Society of Edinburgh 1989 Melbourne I. Department of Mathematics, University of Houston, Houston, TX 77204-3746, U.S.A Chossat P. I.M.S.P., Université de Nice, Pare Valrose, F-06034 Nice Cedex, France Golubitsky M. Department of Mathematics, University of Houston, Houston, TX 77204-3746, U.S.A Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/3-4(1989), 315-345 0308-2105 113:3-4<315 1989 113 PRM https://doi.org/10.1017/S0308210500024173 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500024173 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Melbourne I. Department of Mathematics, University of Houston, Houston, TX 77204-3746, U.S.A NATIONALLICENCE 700 1- Chossat P. I.M.S.P., Université de Nice, Pare Valrose, F-06034 Nice Cedex, France NATIONALLICENCE 700 1- Golubitsky M. Department of Mathematics, University of Houston, Houston, TX 77204-3746, U.S.A NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/3-4(1989), 315-345 0308-2105 113:3-4<315 1989 113 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge