The Existence of ?nite Invariant Measures, Applications to Real 1-dimensional Dynamics
نویسنده
چکیده
A general construction for ?nite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of f n () will imply the existence of a ?nite invariant measure for the map f which is absolutely continuous with respect to , a measure on the phase space describing the sets of measure zero. Furthermore we will discuss suucient conditions for the existence of ?nite invariant absolutely continuous measures for real 1-dimensional dynamical systems.
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. D S ] 1 5 Ja n 19 92 THE EXISTENCE OF σ − FINITE INVARIANT MEASURES , APPLICATIONS TO REAL 1 - DIMENSIONAL DYNAMICS
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...
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