Heteroclinic Attractors: Time Averages and Moduli of Topological Conjugacy

摘要

In this paper we consider heteroclinic 'attractors' (they differ from usualattractors in the sense that they are only attracting from one side) as in an example by Bowen of a smooth (at least C(sup 3)) vector field in the plane with two saddle points and two saddle connections. The eigenvalues of the linearized vector fields at the saddle points are supposed to be so that the cycle, consisting of the two saddle connections, is attracting from the inside. The special property of the example is that for no orbit, converging to this cycle, there is a corresponding 'physical measure'.