# Sensitivity of Uniformly Convergent Mapping Sequences in Non-Autonomous Discrete Dynamical Systems

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1**

**Definition**

**2**

**Definition**

**3**

**Definition**

**4**

**Definition**

**5**

**Definition**

**6**

## 3. The Relation of Chaoticity between ${\mathit{f}}_{\mathbf{1},\infty}$ and Its Limit Map $\mathit{f}$

**Lemma**

**1**

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

**Example**

**1.**

**Example**

**2.**

**Remark**

**1.**

## 4. Some Supplements

**Theorem**

**5.**

**Proof.**

**Corollary**

**1.**

**Remark**

**2.**

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Chaotic behaviors of h in Example 1 with the initial data ${x}_{1}=0.3556$, ${x}_{2}=0.3557$ and $n=3000$.

**Figure 2.**Chaotic behaviors of p in Example 2 with the initial data ${x}_{1}=0.3556$, ${x}_{2}=0.3557$ and $n=6000$.

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**MDPI and ACS Style**

Jiang, Y.; Yang, X.; Lu, T.
Sensitivity of Uniformly Convergent Mapping Sequences in Non-Autonomous Discrete Dynamical Systems. *Fractal Fract.* **2022**, *6*, 319.
https://doi.org/10.3390/fractalfract6060319

**AMA Style**

Jiang Y, Yang X, Lu T.
Sensitivity of Uniformly Convergent Mapping Sequences in Non-Autonomous Discrete Dynamical Systems. *Fractal and Fractional*. 2022; 6(6):319.
https://doi.org/10.3390/fractalfract6060319

**Chicago/Turabian Style**

Jiang, Yongxi, Xiaofang Yang, and Tianxiu Lu.
2022. "Sensitivity of Uniformly Convergent Mapping Sequences in Non-Autonomous Discrete Dynamical Systems" *Fractal and Fractional* 6, no. 6: 319.
https://doi.org/10.3390/fractalfract6060319