Stochastic Properties of Dynamical Systems Arising from (quantum) Spaces and Actions of Groups

TL;DR

This paper reviews recent findings on the stochastic properties of dynamical systems derived from (quantum) spaces and group actions, exploring their transformations, zeta functions, and underlying dynamics.

Contribution

It introduces new insights into the stochastic behavior of dynamical systems associated with quantum spaces and group actions, including analysis of their zeta functions.

Findings

Identification of stochastic properties in quantum space-based dynamical systems

Development of new methods for analyzing zeta functions of these systems

Insights into the impact of group actions on system dynamics

Abstract

We review novel results and investigate actions and transformations of groups and semigroups on (quantum) spaces, present dynamical systems and zeta functions arising from these spaces, actions and transformations, discuss their stochastic properties.