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arXiv · 2501.01134

Incomplete crossing and semi-topological horseshoes

Junfeng Cheng·Xiao-Song Yang
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Abstract

This paper enriches the topological horseshoe theory using finite subshift theory in symbolic dynamical systems, and develops an elementary framework addressing incomplete crossing and semi-horseshoes. Two illustrative examples are provided: one from the perturbed Duffing system and another from a polynomial system proposed by Chen, demonstrating the prevalence of semi-horseshoes in chaotic systems. Moreover, the semi-topological horseshoe theory enhances the detection of chaos and improves the accuracy of topological entropy estimation.

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Junfeng Cheng, Xiao-Song Yang. 2025-01-02. Incomplete crossing and semi-topological horseshoes. https://arxiv.org/abs/2501.01134

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