V.E.Chernyshev

Heteroclinic contours that generate stable chaos

Summary

A new class of invariant sets of relatively simple structure is investigated.
This class consists of heteroclinic cycles of the Lorenz type.

It is shown that if a three-dimensional autonomous system of differential
equations has an invariant set of this class, then the system exhibits chaotic
behavior of trajectories in a neighborhood of this set. This chaotic behavior
is not destroyed by $C^1$ small perturbations, only its topological structure
is changed. Possible bifurcations of the chaotic invariant set generated by a
heteroclinic cycle of the Lorenz type are described.

Russian, 208 pp.; an English version of the Introduction (8 pp.).

AMS classification (AMS2000)

Primary: 37D45
Secondary: 37C29, 37G30, 34C28, 34C37