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 FrechĂ©t 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.


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