Institute for Mathematical Sciences
The Existence of Sigma-Finite Invariant Measures, Applications to Real One-Dimensional Dynamics.
Abstract: A general construction for $\sigma-$finite absolutely continuous invariant measure will be presented. It will be
shown that the local bounded distortion of the Radon-Nykodym
derivatives of $f^n_*(\lambda)$ will imply the existence of a
$\sigma-$finite invariant measure for the map $f$ which is
absolutely continuous with respect to $\lambda$, a measure on
the phase space describing the sets of measure zero.
Furthermore we will discuss sufficient conditions for the
existence of $\sigma-$finite invariant absolutely continuous
measures for real 1-dimensional dynamical systems.
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