arXiv
Open Access
2025
Degree growth of skew pentagram maps
Max Weinreich
Abstrak
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
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