Entropy, Lyapunov exponents and the boundary deformation rate under the action of hyperbolic dynamical systemsстатья
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Дата последнего поиска статьи во внешних источниках: 10 мая 2016 г.
Аннотация:We consider an Anosov diffeomorphism of a Riemannian manifold
and characterize the deformation of the boundary of a small ball
in under the action of in terms of the volume of a small
neighbourhood of divided by the volume of . We prove that the
logarithm of this ratio divided by tends to the sum of the positive
Lyapunov exponents of an arbitrary -invariant ergodic probability
measure a.e. with respect to this measure, provided that increases
not too fast. A statement concerning the measure-theoretic entropy
of is stated as a corollary.