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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.08006 |
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| _version_ | 1866914461337518080 |
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| author | Ji, Haoyang |
| author_facet | Ji, Haoyang |
| contents | In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic stability in the strong sense: convergence of the densities of the stationary measures to the density of the physical measure of the unperturbed map in the $L^1$-norm. This improves the main result in \cite{Me}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08006 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic stability for weakly hyperbolic contracting Lorenz maps Ji, Haoyang Dynamical Systems 37E05, 37H30 In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic stability in the strong sense: convergence of the densities of the stationary measures to the density of the physical measure of the unperturbed map in the $L^1$-norm. This improves the main result in \cite{Me}. |
| title | Stochastic stability for weakly hyperbolic contracting Lorenz maps |
| topic | Dynamical Systems 37E05, 37H30 |
| url | https://arxiv.org/abs/2604.08006 |