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This is a Quantitative Study study.

October 19, 2025Open Access

Finitude of physical measures for Markovian random maps

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The study establishes conditions for the existence of finitely many ergodic, invariant measures in Markovian contexts.
Results indicate that physical measures can be finitely many, covering the phase space almost everywhere under certain conditions.
It employs an i.i.d. framework to extend results from Bernoulli systems to Markovian random dynamical systems.
The investigation reveals that mostly contracting systems with negative Lyapunov exponents yield the desired properties.

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Analysis elucidates conditions for finitely many invariant measures in Markovian systems, suggesting a pathway for random transformations.

Barrientos et al. (2025) studied this question.

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Analysis elucidates conditions for finitely many invariant measures in Markovian systems, suggesting a pathway for random transformations.