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arXiv · 2606.09207

Many coexisting attractors, a case study of the almost-conservative H\'enon map

Corrado Falcolini·Laura Tedeschini-Lalli·James A. Yorke
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Abstract

For dynamical systems in the plane, there can be many periodic attractors coexisting in a bounded region. They become easier to find in systems with small dissipation, which we call ``almost-conservative''. We ask what happens when there are many periodic attractors. That is the vague question we start with. For a test study, we chose the H\'enon map with a tiny dissipation. We tuned the other parameter to yield a case with 50 attracting periodic orbits. They have a total of 4259 periodic points. We describe how these orbits can be organized into families. In addition to two low-period orbits, the remaining 48 orbits can be classified into three families, which we describe in detail.

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Corrado Falcolini, Laura Tedeschini-Lalli, James A. Yorke. 2026-06-08. Many coexisting attractors, a case study of the almost-conservative H\'enon map. https://arxiv.org/abs/2606.09207

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