2001•Journal of Southwest Jiaotong UniversityRequires access

Chaotic Behaviors in Finite Subshifts

Xie Jianhua

Abstract

A necessary and sufficient condition is given for topologically mixed finite subshifts that are described by directed graphs. Based on this result, the spectral decomposition theorems are proved by using permutation canonical forms of nonnegative matrices. The existence of hyperbolic invariant set possessed by the quadratic map is re-examined. Some details missed in the references are provided and a new type of finite subshifts is found.

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Key concepts: Subshift of finite type, Mathematics, Invariant (physics), Permutation (music), Chaotic, Quadratic equation, Set (abstract data type), Pure mathematics