## Transverse bifurcations of homoclinic cycles
and the magnetic dynamo problem

*Physica D* **100** (1997) 85-100

** Pascal Chossat, Martin Krupa, Ian Melbourne and Arnd Scheel **

** Abstract **

Homoclinic cycles exist robustly in dynamical systems with symmetry,
and may undergo various bifurcations, not all of which
have an analogue in the absence of symmetry.
We analyze such a bifurcation, the * transverse bifurcation*, and
uncover a variety of
phenomena that can be distinguished representation-theoretically.
For example, exponentially flat branches of periodic solutions
(a typical feature of bifurcation from homoclinic cycles) occur
for some but not all representations of the symmetry group.
Our study of transverse bifurcations is motivated by the problem
of intermittent dynamos in rotating convection, see
our later paper .

**Postscript file**
or
**pdf file**