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Publicação
Lyapunov exponents and entropy for divergence-free Lipschitz vector fields
Autores
Orientador(es)
Resumo(s)
Let X^0,1( M ) be the subset of divergence-free Lipschitz vector fields defined on a closed Riemannian manifold M endowed with the Lipschitz topology ∥ · ∥_0,1 where ν is the volume measure. Let L be the subset of vector fields satisfying the L-property, a property that implies C^1-regularity ν-almost everywhere. We prove that there exists a residual subset R ⊂ L with respect to ∥·∥0,1 such that Pesin’s entropy formula holds, i.e. for any X ∈ R the metric entropy equals the integral, with respect to ν, of the sum of the positive Lyapunov exponents.
Descrição
Palavras-chave
Volume-preserving flows Lyapunov exponents Metric entropy Lipschitz vector fields
Contexto Educativo
Citação
Bessa, M. Lyapunov exponents and entropy for divergence-free Lipschitz vector fields. European Journal of Mathematics 9, 20 (2023)
Editora
Springer