A Note on the Growth of Periodic Points for Commuting Toral Automorphisms

Table 1

The number of fixed points 𝑁(𝑛₁,𝑛₂) for |𝑛₁|,|𝑛₂|≤4. The columns correspond to 𝑛₁ and the rows correspond to 𝑛₂.

	−4	−3	−2	−1	0	1	2	3	4
4	533	27	203	377	533	448	1261	11857	68411
3	377	91	13	64	91	27	559	3913	21463
2	203	64	13	7	13	13	203	1247	6656
1	27	13	7	1	1	7	64	377	2009
0	533	91	13	1	∞	1	13	91	533
−1	2009	377	64	7	1	1	7	13	27
−2	6656	1247	203	13	13	7	13	64	203
−3	21463	3913	559	27	91	64	13	91	377
−4	68411	11857	1261	448	533	377	203	27	533