Conditioned stochastic stability of equilibrium states on uniformly expanding repellers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908715844632576 |
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| author | Cornudella, Bernat Bassols de Castro, Matheus Manzatto Lamb, Jeroen S. W. |
| author_facet | Cornudella, Bernat Bassols de Castro, Matheus Manzatto Lamb, Jeroen S. W. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_01343 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conditioned stochastic stability of equilibrium states on uniformly expanding repellers Cornudella, Bernat Bassols de Castro, Matheus Manzatto Lamb, Jeroen S. W. Dynamical Systems Probability 47D08, 60J05, 37D20, 37D35, 37D45 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. |
| title | Conditioned stochastic stability of equilibrium states on uniformly expanding repellers |
| topic | Dynamical Systems Probability 47D08, 60J05, 37D20, 37D35, 37D45 |
| url | https://arxiv.org/abs/2405.01343 |