Discrete chaos in Banach spaces. (English) Zbl 1170.37306

Shi, Yuming; Chen, Guanrong

Sci. China, Ser. A 48, No. 2, 222-238 (2005).

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