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This research analyzes the simple spectrum in partially hyperbolic diffeomorphisms, highlighting results related to volumetric dynamics and measures of maximal entropy.
We study the simplicity of the Lyapunov spectrum of partially hyperbolic diffeomorphisms. We prove that a class of volume-preserving partially hyperbolic diffeomorphisms is Cʳ-accumulated by C²-open sets with simple spectrum. Also we prove that a class of partially hyperbolic maps has simple spectrum generically for the measures of maximal entropy. In order to prove these results, we give a criterion for simplicity of the Lyapunov spectrum in terms of periodic points homoclinically related to the invariant measure.
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Marin et al. (2025) studied this question.
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