Đề tài "The Lyapunov exponents of generic volume-preserving and symplectic maps "

We show that the integrated Lyapunov exponents of C 1 volume-preserving diffeomorphisms are simultaneously continuous at a given diffeomorphism only if the corresponding Oseledets splitting is trivial (all Lyapunov exponents are equal to zero) or else dominated (uniform hyperbolicity in the projective bundle) almost everywhere. We deduce a sharp dichotomy for generic volume-preserving diffeomorphisms on any compact manifold:

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10    1    2    05-08-2021