## Discrete chaos in Banach spaces.(English)Zbl 1170.37306

From the abstract: This paper is concerned with chaos in discrete dynamical systems governed by continuously Frechét differentiable maps in Banach spaces. A criterion of chaos induced by a regular nondegenerate homoclinic orbit is established. Chaos of discrete dynamical systems in the $$n$$-dimensional real space is also discussed, with two criteria derived for chaos induced by nondegenerate snap-back repellers, one of which is a modified version of Marotto’s theorem.

### MSC:

 37B99 Topological dynamics 39A11 Stability of difference equations (MSC2000) 37C29 Homoclinic and heteroclinic orbits for dynamical systems 47H99 Nonlinear operators and their properties