Publications
D. Dudko, M. Hlushchanka, and D. Schleicher. A canonical decomposition of postcritically finite rational maps and their maximal expanding quotients. Preprint: arXiv:2209.02800, 2022.
M. Hlushchanka and N. Prochorov. Critically fixed Thurston maps: classification, recognition, and twisting. Preprint: arXiv:2212.14759, 2022.
M. Bonk, M. Hlushchanka, A. Iseli. Eliminating Thurston obstructions and controlling dynamics on curves. Ergod. Theory Dyn. Syst. 2024:1-79. doi:10.1017/etds.2023.114.
M. Hlushchanka. Tischler graphs of critically fixed rational maps and their applications. To appear in the Proceedings of the Simons Symposia on Algebraic, Complex, and Arithmetic Dynamics. Preprint: arXiv:1904.04759, 2019.
M. Hlushchanka and D. Meyer. Exponential growth of some iterated monodromy groups. Proc. Lond. Math. Soc. (3) 116(6):1489–1518, 2018. doi:10.1112/plms.12118.
M. Hlushchanka, Invariant graphs, tilings, and iterated monodromy groups, Ph.D. dissertation, 2017, URN: nbn-resolving.org/urn:nbn:de:gbv:579-opus-1007507.
In preparation
1. L. Geyer and M. Hlushchanka. Classification of critically fixed anti-Thurston maps.
2. M. Bonk, M. Hlushchanka, and D. Meyer. Conformal dimension and quasi-visual approximations.
3. M. Hlushchanka. A criterion for exponential growth of iterated monodromy groups.