The Mean Sensitivity and Mean Equicontinuity in Uniform Spaces

Wu, Xinxing; Liang, Shudi; Ma, Xin; Lu, Tianxiu; Ahmadi, Seyyed Alireza

doi:10.1142/s0218127420501229

Cited by 16 publications

(6 citation statements)

References 35 publications

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“…1.02 results about equicontinuity to the uniform spaces; Das et al [13] generalized spectral decomposition theorem to the uniform spaces; The authors of [3] generalized concepts of entropy points, expansivity and the shadowing property for dynamical systems on uniform spaces and obtained a relation between the topological shadowing property and the positive uniform entropy. For more results on properties of dynamical systems in purely topological terms, one is referred to [2,14,22,[26][27][28].…”

Section: Generalized Many Knownmentioning

confidence: 99%

Recurrent sets for endomorphisms of topological groups

AHMADI,

JAMALZADEH

2024

MATHEMATICA

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This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent points and chain transitive component of the identity are topological subgroups. Furthermore, we show that some dynamical properties are induced by the original system on quotient spaces. These results link an algebraic property to a dynamical property.

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Section: Generalized Many Knownmentioning

confidence: 99%

Recurrent sets for endomorphisms of topological groups

AHMADI,

JAMALZADEH

2024

MATHEMATICA

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“…In Climate Change, e.g., Lyu et al (2020). In Complexity Systems, e.g., Wu et al (2020). In Psychology, e.g., Wenzel and Kubiak (2020).…”

Section: Introductionmentioning

confidence: 99%

Averages: There is Still Something to Learn

Curto

2021

Comput Econ

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The common way to deal with outliers in empirical Economics and Finance is to delete them, either by trimming or winsorizing, or by computing statistics robust to outliers. However, due to their importance, there are situations where the exclusion of these observations is not reasonable and may even be counterproductive. For example, should we exclude the very high stock prices of Amazon and Google from an empirical analysis? Even if the purpose is to compute an average of tech stock prices, does it make economic and financial sense? Maybe not. A solution that would keep the two companies in the data set and yet not penalize the higher observations as much as the median, harmonic and geometric averages, mightwere such a solution to be available-constitute an attractive alternative. In this paper we propose and analyze a modified measure, the adjusted median, where the influence of the outlying observations, while not as high as in the arithmetic average would, however, give more weight to the outlying observations than the median, harmonic and geometric averages. Monte Carlo simulations and bootstrapping real financial data confirm how useful the adjusted median could be.

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“…[6] proved that for continuous functions on intervals in R, transitivity implies chaos. Since the end of the 20th century, transitivity and sensitivity has been hotly discussed, see [7][8][9][10][11][12][13], and others. Especially, the convergence of chaotic functions has attracted the attention of many scholars.…”

Section: Introductionmentioning

confidence: 99%