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M TSUJII, *POSITIVE LYAPUNOV EXPONENTS IN FAMILIES OF ONE-DIMENSIONAL DYNAMIC-SYSTEMS*, INVENTIONES MATHEMATICAE, Vol.111, No.1, pp.113-137, 1993.01, We give a generalization of Jakobson's theorem [Ja] and a precise estimate for the density of parameters corresponding to systems with absolutely continuous invariant measures.. |

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M Tsujii, *On continuity of Bowen-Ruelle-Sinai measures in families of one dimensional maps*, COMMUNICATIONS IN MATHEMATICAL PHYSICS, 10.1007/BF02102427, Vol.177, No.1, pp.1-11, 1996.03, Let us consider a family of maps Q(a)(x) = ax(1 - x) from the unit interval [0, 1] to itself, where a is an element of [0, 4] is the parameter. We show that, for any beta < 2, there exists a subset E There Exists 4 in [0,4] with the properties (1) Leb([4 - epsilon,4] - E) < epsilon(beta) for sufficiently small epsilon > 0, (2) Q(a) admits an absolutely continuous BRS measure mu(a), when a is an element of E, and (3) mu(a) converges to the measure mu(4) as a tends to 4 on the set E. Also we give some generalization of this results.. |

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M Tsujii, *Absolutely continuous invariant measures for piecewise real-analytic expanding maps on the plane*, COMMUNICATIONS IN MATHEMATICAL PHYSICS, Vol.208, No.3, pp.605-622, 2000.01, We prove the existence of absolutely continuous invariant measures for piecewise real-analytic expanding maps on bounded regions in the plane.. |