zbMATH — the first resource for mathematics

Homoclinic orbits and Bernoulli bundles in almost periodic systems. (English) Zbl 0636.34037
Oscillation, bifurcation and chaos, Proc. Annu. Semin., Toronto/Can. 1986, CMS Conf. Proc. 8, 527-544 (1987).
[For the entire collection see Zbl 0618.00006.]
The authors announce some results concerning the method of detecting transversal homoclinic orbits of two-dimensional dynamical systems of the following type: \(\dot x=F(x)+\epsilon f(t),\) \(x\in {\mathbb{R}}^ 2.\) These results are generalizations of the known Melnikov’s method and yield the generalization of the almost periodic system, horseshoe invariant set of Smale. The authors introduce some new notions: skew product system and Bernoulli bundle.
Reviewer: V.B.Marenich

34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
37C55 Periodic and quasi-periodic flows and diffeomorphisms
37D99 Dynamical systems with hyperbolic behavior
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior