The existence of sigma-finite invariant measures, applications to real one-dimensional dynamics

Details The existence of sigma-finite invariant measures, applications to real one-dimensional dynamics The existence of sigma-finite invariant measures, applications to real one-dimensional dynamics

1992-01-15

arxiv.org/abs/math/9201300v1

Mathematics

Dynamical Systems

Scientific paper

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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