The Pesin entropy formula for diffeomorphisms with dominated splitting
2014 ◽
Vol 35
(3)
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pp. 737-761
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Keyword(s):
AbstractFor any$C^1$diffeomorphism with dominated splitting, we consider a non-empty set of invariant measures that describes the asymptotic statistics of Lebesgue-almost all orbits. They are the limits of convergent subsequences of averages of the Dirac delta measures supported on those orbits. We prove that the metric entropy of each of these measures is bounded from below by the sum of the Lyapunov exponents on the dominating sub-bundle. As a consequence, if those exponents are non-negative, and if the exponents on the dominated sub-bundle are non-positive, those measures satisfy the Pesin entropy formula.
2013 ◽
Vol 33
(9)
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pp. 4123-4155
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1996 ◽
Vol 16
(4)
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pp. 735-749
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2002 ◽
Vol 12
(10)
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pp. 2087-2103
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2021 ◽
Vol 19
(2)
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pp. 155-187
2006 ◽
Vol 15
(1)
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pp. 61-71
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