EMPIRICAL INVARIANCE PRINCIPLE FOR ERGODIC TORUS AUTOMORPHISMS: GENERICITY
2008 ◽
Vol 08
(02)
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pp. 173-195
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Keyword(s):
We consider the dynamical system given by an algebraic ergodic automorphism T on a torus. We study a Central Limit Theorem for the empirical process associated to the stationary process (f◦Ti)i∈ℕ, where f is a given ℝ-valued function. We give a sufficient condition on f for this Central Limit Theorem to hold. In the second part, we prove that the distribution function of a Morse function is continuously differentiable if the dimension of the manifold is at least three and Hölder continuous if the dimension is one or two. As a consequence, the Morse functions satisfy the empirical invariance principle, which is therefore generically verified.
2021 ◽
Vol 36
(2)
◽
pp. 243-255
Keyword(s):
2012 ◽
Vol 27
(1)
◽
pp. 249-277
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Keyword(s):
1998 ◽
Vol 326
(1)
◽
pp. 87-92
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1985 ◽
Vol 5
(4)
◽
pp. 625-640
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2014 ◽
Vol 124
(11)
◽
pp. 3769-3781
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2017 ◽
Vol 71
(1)
◽
pp. 11
Keyword(s):