幂零流形上自映射的点态原像熵的可加性

黄保军

数学学报 ›› 2019, Vol. 62 ›› Issue (6) : 913-922.

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数学学报 ›› 2019, Vol. 62 ›› Issue (6) : 913-922. DOI: 10.12386/A2019sxxb0082
论文

幂零流形上自映射的点态原像熵的可加性

    黄保军1,2
作者信息 +

The Additivity of Pointwise Preimage Entropy for Selfmaps on Nilmanifolds

    Bao Jun HUANG1,2
Author information +
文章历史 +

摘要

类似于拓扑熵,点态原像熵作为动力系统的不变量,也度量了紧度量空间上系统的复杂性.但至今不知其性质与拓扑熵是否完全一致,例如映射笛卡尔积的点态原像熵的可加性等.本文将把环面自映射笛卡尔积的点态原像熵的可加性,推广到紧幂零流形自映射的情形.

Abstract

Pointwise preimage entropy is similar to topological entropy but, in general, their properties are not completely coincident such as additivity of under Cartesian product. In this paper we show that the description of the additivity of pointwise preimage entropy of the torus maps under Cartesian product given by myself extends to the case of the maps of compact nilmanifolds.

关键词

点态原像熵 / 可加性 / 幂零流形

Key words

pointwise preimage entropy / additivity / nilmanifolds

引用本文

导出引用
黄保军. 幂零流形上自映射的点态原像熵的可加性. 数学学报, 2019, 62(6): 913-922 https://doi.org/10.12386/A2019sxxb0082
Bao Jun HUANG. The Additivity of Pointwise Preimage Entropy for Selfmaps on Nilmanifolds. Acta Mathematica Sinica, Chinese Series, 2019, 62(6): 913-922 https://doi.org/10.12386/A2019sxxb0082

参考文献

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