Exponential mixing for the multidimensional Lorenz attractor

The multidimensional Lorenz attractor is the sectional-hyperbolic attractor introduced by Bonatti, Pumariño and Viana. Multidimensional Lorenz mixing conjecture. The multidimensional Lorenz attractor is exponentially mixing. Moreover, this conclusion holds for an open and dense subset of all sectional-hyperbolic attracting sets. Exponential mixing is known for physical measures in some Anosov-flow settings, whereas the asserted result for the multidimensional Lorenz attractor and an open dense subset of higher-dimensional sectional-hyperbolic attracting sets remains open.

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Primary source

Vitor Araujo and Edvan Trindade, “Robust Exponential Mixing and Convergence to Equilibrium for Singular Hyperbolic Attracting Sets”, arXiv:2012.13183 (2021).

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