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arXiv · 2405.17122

Relative stationary dynamical systems

Tattwamasi Amrutam·Martin Klötzer·Hanna Oppelmayer
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Abstract

Let $G$ be a locally compact second countable group equipped with an admissible non-degenerate Borel probability measure $\mu$. We generalize the notion of $\mu$-stationary systems to $\mu$-stationary $G$-factor maps $\pi: (X,\nu)\to (Y,\eta)$. For these stationary relations between dynamical systems, we provide a structure theorem, which generalizes the structure theorem of Furstenberg-Glasner. Furthermore, we show the existence and uniqueness of a relative version of the Poisson boundary in this setup.

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Tattwamasi Amrutam, Martin Klötzer, Hanna Oppelmayer. 2024-05-27. Relative stationary dynamical systems. https://arxiv.org/abs/2405.17122

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