| 一维映射迭代根的非单调性及光滑性 |
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| 引用本文： | 刘鎏,余志恒,曾莹莹,张伟年.一维映射迭代根的非单调性及光滑性[J].中国科学:数学,2021(1). |
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| 作者姓名： | 刘鎏 余志恒 曾莹莹 张伟年 |
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| 作者单位： | 西南交通大学数学学院;四川师范大学数学科学学院、可视化计算与虚拟现实四川省重点实验室;四川大学数学学院 |
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| 基金项目： | 国家自然科学基金(批准号:11501471,11701476,11501394,11701400,11821001和11831012);四川师范大学Laurent数学研究中心和可视化计算与虚拟现实四川省重点实验室资助项目。 |
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| 摘 要： | 迭代根问题是动力系统嵌入流问题的弱问题,是动态插值方法的基础.然而,即使是对一维映射,迭代根的非单调性和全局光滑性都是困难的问题.本文介绍这方面的若干新结果,尤其是关于严格逐段单调连续函数的连续迭代根的存在性和构造,以及迭代根局部光滑与全局光滑的新进展.最后给出多项式迭代根这类既严格逐段单调又具光滑性的迭代根的存在条件及计算方法.
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| 关 键 词： | 迭代根 严格逐段单调 非单调高度 特征区间 光滑性 |
Non-monotonicity and smoothness of iterative roots of one-dimensional mapping |
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| Liu Liu,Zhiheng Yu,Yingying Zeng,Weinian Zhang.Non-monotonicity and smoothness of iterative roots of one-dimensional mapping[J].Scientia Sinica Mathemation,2021(1). |
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| Authors: | Liu Liu Zhiheng Yu Yingying Zeng Weinian Zhang |
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| Abstract: | The problem of iterative roots is a weak version of embedding flows,which is a basis of dynamic interpolation.However,even for one-dimensional mappings,it is still difficult to discuss the non-monotonicity and smoothness of their iterative roots.In this paper,some new results are introduced,especially for the existence and construction of continuous iterative roots of strictly piecewise monotone and continuous mappings,and for smoothness of iterative roots about local and global cases.Finally,as a special class of strictly piecewise monotone and smooth mappings,polynomials are discussed and the conditions of existence with calculation methods of their iterative roots are given. |
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| Keywords: | iterative root strictly piecewise monotone non-monotonicity height characteristic interval smoothness |
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