Discrete chaos in Banach spaces

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)22_Publication in policy or professional journal

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Detail(s)

Original languageEnglish
Pages (from-to)222-238
Journal / PublicationScience in China, Series A: Mathematics
Volume48
Issue number2
Publication statusPublished - Feb 2005

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. In particular, a necessary and sufficient condition is obtained for an expanding fixed point of a differentiable map in a general Banach space and in an n-dimensional real space, respectively. It completely solves a long-standing puzzle about the relationship between the expansion of a continuously differentiable map near a fixed point in an n-dimensional real space and the eigenvalues of the Jacobi matrix of the map at the fixed point.

Research Area(s)

  • Banach space, Chaos, Discrete dynamical system, Marotto's theorem

Citation Format(s)

Discrete chaos in Banach spaces. / Shi, Yuming; Chen, Guanrong.

In: Science in China, Series A: Mathematics, Vol. 48, No. 2, 02.2005, p. 222-238.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)22_Publication in policy or professional journal