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A planar topological horseshoe theory with applications to computer verifications of chaos

2005; Institute of Physics; Volume: 38; Issue: 19 Linguagem: Inglês

10.1088/0305-4470/38/19/008

1361-6447

Xiao‐Song Yang, Huimin Li, Yan Huang,

Mathematical Dynamics and Fractals

In this paper, we present an elementary theory on the existence and robustness of horseshoes under perturbations in terms of stability of crossing. The framework is developed in the setting of 2D Euclidean space but can be generalized to metric spaces. As an application, we give a rigorous verification of the existence of a horseshoe in the Ikeda map.