Abstract
In this paper we shall consider random perturbations of uniformly hyperbolic dynamical systems. This question has been discussed in the physical literature mostly for flows6. A review of some rigorous results is given by Ventsel and Freidlin5. Our aim is to give some precise information about the invariant measure in the case of discrete hyperbolic systems2. We shall in particular show under some precise hypothesis that the invariant measure can be represented as an asymptotic series in the amplitude of the noise. We shall not aim at the full generality of this result but rather stay within strong hypothesis to make the exposition as simple as possible. Note however that the general hypothesis needed to prove this result are yet unknown. At several points of the proof we shall meet some technical conditions which can probably be lifted at the expense of some work.
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© 1988 Plenum Press, New York
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Collet, P. (1988). Stochastic Perturbations of the Invariant Measure of Some Hyperbolic Dynamical Systems. In: Gallavotti, G., Zweifel, P.F. (eds) Nonlinear Evolution and Chaotic Phenomena. NATO ASI Series, vol 176. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1017-4_5
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DOI: https://doi.org/10.1007/978-1-4613-1017-4_5
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