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Zbl 1170.37306
Shi, Yuming; Chen, Guanrong
Discrete chaos in Banach spaces. (English)
[J] Sci. China, Ser. A 48, No. 2, 222-238 (2005). ISSN 1006-9283; ISSN 1862-2763/e

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 2000:: *37B99 Topological dynamics
39A11 Stability of difference equations
37C29 Homoclinic and heteroclinic orbits
47H99 Nonlinear operators

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