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arXiv · 2512.10062

Degree growth of skew pentagram maps

Max Weinreich
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Abstract

Skew pentagram maps act on polygons by intersecting diagonals of different lengths. They were introduced by Khesin-Soloviev in 2015 as conjecturally non-integrable generalizations of the pentagram map, a well-known integrable system. In this paper, we show that certain skew pentagram maps have exponential degree growth and no preserved fibration. To formalize this, we introduce a general notion of first dynamical degree for lattice maps, or shift-invariant self-maps of $(\mathbb{P}^N)^\mathbb{Z}$. We show that the dynamical degree of any equal-length pentagram map is 1, but that there are infinitely many skew pentagram maps with dynamical degree 4.

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Max Weinreich. 2025-12-10. Degree growth of skew pentagram maps. https://arxiv.org/abs/2512.10062

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