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Structure and f -Dependence of the A.C.I.M. for a Unimodal Map f of Misiurewicz Type

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Abstract

By using a suitable Banach space on which we let the transfer operator act, we make a detailed study of the ergodic theory of a unimodal map f of the interval in the Misiurewicz case. We show in particular that the absolutely continuous invariant measure ρ can be written as the sum of 1/square root spikes along the critical orbit, plus a continuous background. We conclude by a discussion of the sense in which the map \({f\mapsto\rho}\) may be differentiable.

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Authors and Affiliations

  1. Mathematics Department, Rutgers University, Piscataway, NJ, 08854, USA

    David Ruelle

  2. IHES, 35 route de Chartres, 91440, Bures sur Yvette, France

    David Ruelle

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  1. David Ruelle
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Correspondence to David Ruelle.

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Communicated by G. Gallavotti

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Ruelle, D. Structure and f -Dependence of the A.C.I.M. for a Unimodal Map f of Misiurewicz Type. Commun. Math. Phys. 287, 1039–1070 (2009). https://doi.org/10.1007/s00220-008-0637-8

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  • DOI: https://doi.org/10.1007/s00220-008-0637-8

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