LARGE ENTROPY MEASURES OF H ´ ENON-LIKE MAPS
We study the Lyapounov exponent of ergodic invariant measures for Henon-like maps under
appropriate entropy conditions. Specifically, we consider an ergodic measure ν for a Henon-like
map f satisfying h ν (f) > logd +
p−1 when d
+
p−1 < d. We establish that ν has at least p strictly positive
Lyapounov exponents bounded below by
? h
ν (f) − logd +
p−1
?
/2k. These results provide insight into
the interplay between entropy, degree growth, and Lyapounov exponents in the dynamical behavior
of Henon-like maps.
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