On the Holomorphic and Random Dynamics for some examples of higher rank Free Groups generated by H\'enon type maps
Abstract
We study the Holomorphic and Random Dynamics of some rank 2 free groups generated by two H\'enon type maps. For these simply constructed examples we prove that the Fatou set is non-empty and that the stationary measures are supported on a compact set. With some further care this allows us to construct examples having no stationary measures. These examples illustrate the types of phenomena that may arise when studying holomorphic group actions on non-compact manifolds.
Cite
@article{arxiv.2602.02324,
title = {On the Holomorphic and Random Dynamics for some examples of higher rank Free Groups generated by H\'enon type maps},
author = {Andres Enrique Quintero Santander},
journal= {arXiv preprint arXiv:2602.02324},
year = {2026}
}
Comments
This is the author's accepted manuscript of the contribution. The Version of Record of this contribution will be published in Analysis and PDE in Developing Countries: Proceedings of the ISAAC-ICMAM Conference, 2025. The Version of Record will be made available online upon publication