## Abstract

Motivated by problems in equivariant dynamics and connection selection in heteroclinic networks,
Ashwin and Field investigated the product of planar dynamics where
one at least of the factors was a planar homoclinic attractor. However, they were only able to obtain
partial results in the case of a product of two planar homoclinic attractors. We give general results for the
product of planar homoclinic and heteroclinic attractors. We show that the likely limit set of the basin of
attraction of the product of two planar heteroclinic attractors is always the unique one-dimensional heteroclinic network
which covers the heteroclinic attractors in the factors.
The method we use is general and likely to
apply to products of higher dimensional heteroclinic attractors as well as to situations where the product structure is
broken but the cycles are preserved.
For preprint,
e-mail: mikefield@gmail.com or Michael.J.Field@rice.edu

Professor Mike Field

Department of Mathematics

Rice University

6100 S Main St

Houston

TX 77005-1892