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arXiv · 2405.01343

Conditioned stochastic stability of equilibrium states on uniformly expanding repellers

Bernat Bassols Cornudella·Matheus Manzatto de Castro·Jeroen S. W. Lamb
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Abstract

We propose a notion of conditioned stochastic stability of invariant measures on repellers: we consider whether quasi-ergodic measures of absorbing Markov processes, generated by random perturbations of the deterministic dynamics and conditioned upon survival in a neighbourhood of a repeller, converge to an invariant measure in the zero-noise limit. Under suitable choices of the random perturbation, we find that equilibrium states on uniformly expanding repellers are conditioned stochastically stable. In the process, we establish a rigorous foundation for the existence of ``natural measures'', which were proposed by Kantz and Grassberger in 1984 to aid the understanding of chaotic transients.

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Bernat Bassols Cornudella, Matheus Manzatto de Castro, Jeroen S. W. Lamb. 2025-12-17. Conditioned stochastic stability of equilibrium states on uniformly expanding repellers. https://doi.org/10.1017/etds.2026.10334

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