Abstract:Let $S_g$ be the closed surface of genus $g$, $\mathcal{L}$ be the infinite Jacob's ladder surface, and $\mathrm{Map}(S)$ denote the mapping class group of a surface $S$. Let $q_g:\mathcal{L}\to S_g$ be the regular infinite-sheeted cover with deck transformation group $\mathbb{Z}$. In this paper, we show the existence of ``pseudo-Anosov-like'' maps on $\mathcal{L}$ that arise as the lifts of Penner-type pseudo-Anosov maps on $S_g$ under the cover $q_g$. Furthermore, we establish that these lifts are topologically transitive, mixing, and support null recurrent dynamics. Moreover, we present concrete examples of infinite families of such maps on $\mathcal{L}$.
From: Nikita Agarwal [view email]
[v1]
Sun, 24 Aug 2025 02:56:05 UTC (74 KB)
[v2]
Sat, 18 Jul 2026 05:40:08 UTC (84 KB)
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