Replete unimodal function and other conceptions are defined. It is proved that for any continuous function φ, if φ has a unimodal orbit , then φ has all unimodal orbits whose types precede the orbit type of. They a...Replete unimodal function and other conceptions are defined. It is proved that for any continuous function φ, if φ has a unimodal orbit , then φ has all unimodal orbits whose types precede the orbit type of. They are altogether distributed on a compact subset X of I. The restriction φ|X of φ to X is a replete unimodal function. Moreover, an ordered classification φ of the function space C°(I,R) is given. It is a refinement of the famous Sarkovskii’s ordered classification F, and also a generalization of the conclusion obtained by Bhatia and Egerland not long ago.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Replete unimodal function and other conceptions are defined. It is proved that for any continuous function φ, if φ has a unimodal orbit , then φ has all unimodal orbits whose types precede the orbit type of. They are altogether distributed on a compact subset X of I. The restriction φ|X of φ to X is a replete unimodal function. Moreover, an ordered classification φ of the function space C°(I,R) is given. It is a refinement of the famous Sarkovskii’s ordered classification F, and also a generalization of the conclusion obtained by Bhatia and Egerland not long ago.
