Abstract
Let τ: [0, 1]→[0, 1] be a piecewise monotonic, nonexpanding map which has an invariant densityg and is topologically conjugate to a piecewise monotonic, expanding map, where the conjugacy is absolutely continuous. An effective, computable method is presented for approximatingg.
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References
P. Góra and A. Boyarsky, Compactness of invariant densities for families of expanding, piecewise monotonic transformations, preprint.
M. Misiurewicz, Absolutely continuous measures for certain maps of an interval,Publ. Math. IHES 53:17 (1981).
M. Blank, On the conjugacy of certain class of homogeneous endomorphisms to the class of piecewise monotonic maps,Russ. Math. Sun. 40:211 (1985).
A. Boyarsky and M. Scarowsky, A class of transformations which have unique absolutely invariant measures,Trans. Am. Math. Soc. 255:243 (1979).
M. Misiurewicz, private communication.
A. Boyarsky, A matrix method for estimating the Lyapunov exponent of one-dimensional systems,J. Slat. Phys. 50:213 (1988).
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Góra, P., Boyarsky, A. & Proppe, H. Constructive approximations to densities invariant under nonexpanding transformations. J Stat Phys 51, 179–194 (1988). https://doi.org/10.1007/BF01015325
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DOI: https://doi.org/10.1007/BF01015325