- 07-238 David Ruelle
- Structure and f-dependence of the a.c.i.m. for a unimodal map f of Misiurewicz type.
Oct 10, 07
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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 $\rho$ 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.