Ergodicity and Algebraicity of the Fast and Slow Triangle Maps
Published in Ergodic Theory and Dynamical Systems, 2026
Based on my senior thesis, this paper proves that both the fast and slow versions of the triangle map — a multidimensional continued fraction algorithm — are ergodic in every dimension, resolving a conjecture of Messaoudi, Nogueira, and Schweiger. Joint work with my advisor, Thomas Garrity. Published online August 2025 and in print in the January 2026 issue (Vol. 46, No. 1) of Ergodic Theory and Dynamical Systems.
Recommended citation: Garrity, T. and Lehmann Duke, J. (2026). "Ergodicity and algebraicity of the fast and slow triangle maps." Ergodic Theory and Dynamical Systems, 46(1), 93-127. https://doi.org/10.1017/etds.2025.10198
Download Paper