收缩同构的诱导映射阴影

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-10-21 DOI:10.1016/j.jmaa.2024.128983

W. Jung , M. Lee , C.A. Morales

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引用次数: 0

摘要

设 f:X→X 是具有正直径的度量空间的收缩同构。我们证明，在配有普罗霍罗夫度量的概率度量空间中，诱导映射 f⁎ 不具有阴影性质。然而，如果 X 是波兰的，那么 f⁎ 对 Wasserstein 空间的限制就具有广义阴影性质，正如 Boyarsky 和 Gora [4] 所说的那样，是关于 Kantorovich-Rubinstein 和 Prokhorov 度量的。

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Shadowing of the induced map for contracting homeomorphisms

Let

f : X \to X

be a contracting homeomorphism of a metric space with positive diameter. We prove that the induced map

f_{⁎}

in the space of probability measures equipped with the Prokhorov metric does not have the shadowing property. However, if X is Polish, then the restriction of

f_{⁎}

to the Wasserstein space has the generalized shadowing property as per Boyarsky and Gora [4], concerning the Kantorovich-Rubinstein and Prokhorov metrics.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.