Invariant measures for interval maps with critical points and singularities

Mathematics – Dynamical Systems

Scientific paper

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15 pages, 1 Figure

Scientific paper

We prove that, under a mild summability condition on the growth of the
derivative on critical orbits any piecewise monotone interval map possibly
containing discontinuities and singularities with infinite derivative (cusp
map) admits an ergodic invariant probability measures which is absolutely
continuous with respect to Lebesgue measure.

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