The existence of sigma-finite invariant measures, applications to real one-dimensional dynamics
Marco Martens
Abstract
A general construction for σ-finite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of fn*(λ) will imply the existence of a σ-finite invariant measure for the map f which is absolutely continuous with respect to λ, a measure on the phase space describing the sets of measure zero. Furthermore we will discuss sufficient conditions for the existence of σ-finite invariant absolutely continuous measures for real 1-dimensional dynamical systems.
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