Symbolic dynamics for a kinds of piecewise smooth maps

Jicheng Duan; Zhouchao Wei; Denghui Li; Han Su; Celso Grebogi

Symbolic dynamics for a kinds of piecewise smooth maps

Jicheng Duan, Zhouchao Wei, Denghui Li, Han Su, Celso Grebogi

Research output: Contribution to journal › Article › peer-review

Abstract

Symbolic dynamics is effective for the classification of orbital types and their complexity in one dimensional maps. In this paper, techniques of symbolic dynamics are used to analyze the chaotic dynamical properties of a two-parameter family of piecewise smooth unimodal maps with one break point. Boundary crisis and interior crisis are described via the kneading sequences, while for the period-3 window, a subshift of finite type is constructed. In addition, based on the symbolic model, the topological entropy of the map is computed, and the existence of chaotic sets of Smale horseshoe type is also proved.

Original language	English
Journal	Discrete and Continuous Dynamical Systems - Series S
Publication status	Accepted/In press - 25 Mar 2024

Bibliographical note

Acknowledgments
We sincerely thank the people who give valuable comments. The paper is supported by the National Natural Science Foundation of China (NNSFC) (Nos. 12362002 and 12172340), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (Nos. G1323523061 and G1323523041), and the Young Top-notch Talent Cultivation Program of Hubei Province.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Keywords

Piecewise smooth ma
symbolic dynamics
crises
topological entropy
Smale horseshoe

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Cite this

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abstract = "Symbolic dynamics is effective for the classification of orbital types and their complexity in one dimensional maps. In this paper, techniques of symbolic dynamics are used to analyze the chaotic dynamical properties of a two-parameter family of piecewise smooth unimodal maps with one break point. Boundary crisis and interior crisis are described via the kneading sequences, while for the period-3 window, a subshift of finite type is constructed. In addition, based on the symbolic model, the topological entropy of the map is computed, and the existence of chaotic sets of Smale horseshoe type is also proved.",

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AU - Grebogi, Celso

N1 - Acknowledgments We sincerely thank the people who give valuable comments. The paper is supported by the National Natural Science Foundation of China (NNSFC) (Nos. 12362002 and 12172340), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (Nos. G1323523061 and G1323523041), and the Young Top-notch Talent Cultivation Program of Hubei Province.

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N2 - Symbolic dynamics is effective for the classification of orbital types and their complexity in one dimensional maps. In this paper, techniques of symbolic dynamics are used to analyze the chaotic dynamical properties of a two-parameter family of piecewise smooth unimodal maps with one break point. Boundary crisis and interior crisis are described via the kneading sequences, while for the period-3 window, a subshift of finite type is constructed. In addition, based on the symbolic model, the topological entropy of the map is computed, and the existence of chaotic sets of Smale horseshoe type is also proved.

AB - Symbolic dynamics is effective for the classification of orbital types and their complexity in one dimensional maps. In this paper, techniques of symbolic dynamics are used to analyze the chaotic dynamical properties of a two-parameter family of piecewise smooth unimodal maps with one break point. Boundary crisis and interior crisis are described via the kneading sequences, while for the period-3 window, a subshift of finite type is constructed. In addition, based on the symbolic model, the topological entropy of the map is computed, and the existence of chaotic sets of Smale horseshoe type is also proved.

KW - Piecewise smooth ma

KW - symbolic dynamics

KW - crises

KW - topological entropy

KW - Smale horseshoe

M3 - Article

SN - 1937-1632

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

ER -

Symbolic dynamics for a kinds of piecewise smooth maps

Abstract

Bibliographical note

Data Availability Statement

Keywords

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