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<p>The dynamics that necessarily coexists with a homoclinic orbit is captured by its dynamical core.In this work we characterize the dynamical core of a broad class of homoclinic orbits in the Smale horseshoe,specifically those with decorations of three types: maximal, P-lists and star decorations.For each of these families, we construct an explicit pruning region whose survival set — consisting of all symbolic sequences whose orbits avoid the region under the shift — coincides with the dynamical core.This provides a unified symbolic description of the forced dynamics and establishes a frameworkfor computing dynamical invariants such as topological entropy.</p>

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Computing the Dynamical Core of Horseshoe Homoclinic Orbits

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Valentín Mendoza

摘要

The dynamics that necessarily coexists with a homoclinic orbit is captured by its dynamical core.In this work we characterize the dynamical core of a broad class of homoclinic orbits in the Smale horseshoe,specifically those with decorations of three types: maximal, P-lists and star decorations.For each of these families, we construct an explicit pruning region whose survival set — consisting of all symbolic sequences whose orbits avoid the region under the shift — coincides with the dynamical core.This provides a unified symbolic description of the forced dynamics and establishes a frameworkfor computing dynamical invariants such as topological entropy.