 97380 V. Baladi, C. Bonatti, and B. Schmitt
 Abnormal escape rates from nonuniformly hyperbolic
sets
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Jun 27, 97

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Abstract. Consider a $C^{1+\epsilon}$ diffeomorphism
$f$ having a uniformly hyperbolic compact invariant set
$\Omega$, maximal invariant in some small neighbourhood of itself.
The asymptotic exponential rate of escape from any
small enough neighbourhood of $\Omega$ is given by the topological
pressure of $\log J^u f$ on $\Omega$ (BowenRuelle [1975]).
It has been conjectured (EckmannRuelle [1985])
that this property, formulated in terms of escape
from the support $\Omega$ of a (generalized SRB) measure,
using its entropy and positive Lyapunov exponents, holds
more generally.
We present a simple $C^\infty$ twodimensional counterexample,
constructed by a surgery using a Bowentype hyperbolic saddle
attractor as the basic plug.
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