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arXiv · 2603.21603

An algorithm to detect and rigorously verify blenders

Andy Hammerlindl·Natalia McAlister·Warwick Tucker
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Abstract

We present a characterisation of blenders based on mapping properties of certain sets of curves that can be rigorously verified by computer-assisted methods. We develop an algorithm to construct these sets of curves that requires only a rough approximation of the strong unstable direction in a prescribed region. Since our approach does not rely on precise data, such as the exact location of invariant manifolds or fixed points, it provides a systematic framework to verify blenders in explicit examples. Here, we apply this framework to rigorously verify that a family of three-dimensional Hénon-like maps presents blenders.

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Andy Hammerlindl, Natalia McAlister, Warwick Tucker. 2026-08-25. An algorithm to detect and rigorously verify blenders. https://arxiv.org/abs/2603.21603

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