ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 58e, Lauterbach, Reiner, Weierstrass-Institute for Appl. Anal. Stoch. ,Berlin, Germany Chossat, Pascal, Insitute Nonlinéaire de Nice, Sophia-Antipolis, France Guyard, Frédéric, Weierstrass-Institute for Appl. Anal. Stoch., Berlin, Germany Intermittent dynamics and symmetry Intermittent behaviour can be caused by heteroclinic cycles, that means by a set of equilibria ξ_{1}, …, ξ_{s} and connecting orbits u_{1}(t), …, u_{s}(t), such that ω(u_{i}) = ξ_{i+1} and α(u_{i}) = ξ_{i}, where we compute mod s. Such cycles do not occur in generic flows, however they can be caused by symmetry. We want to explore a specific system which is motivated from geophysics and show that such cycles occur. We observe that our cycle is embedded in a very complicated set. We study its stability and give an interpretation of our results for the motivating problem. Crucial for our analysis is the interplay between dynamics and geometry.