Abstract
Abstract
Under certain conditions, we construct a countable Markov partition for pointwise hyperbolic diffeomorphism
$f:M\rightarrow M$
on an open invariant subset
$O\subset M$
, which allows the Lyapunov exponents to be zero. From this partition, we define a symbolic extension that is finite-to-one and onto a subset of O that carries the same finite f-invariant measures as O. Our method relies upon shadowing theory of a recurrent-pointwise-pseudo-orbit that we introduce. As a canonical application, we estimate the number of closed orbits for f.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Chongqing Municipality
Publisher
Cambridge University Press (CUP)
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