Titlebook: Laws of Chaos; Invariant Measures a Abraham Boyarsky,Paweł Góra Book 19971st edition Springer Science+Business Media New York 1997 Generato

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Book 19971st editionexhibit strange behavior, Poincare undermined the founda­ tions of Newtonian physics and opened a window to the modern theory of nonlinear dynamics and chaos. Although in the 1930s and 1940s strange behavior was observed in many physical systems, the notion that this phenomenon was inherent in deter

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Other Existence Results,lklore Theorem which established the existence of absolutely continuous invariant measure for Markov transformations. Inspired by number theoretical questions Rényi [1957] proved the first version of this theorem for piecewise onto transformations. We follow closely the development in [Adler and Fla

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Spectral Decomposition of the Frobenius-Perron Operator,or. In this chapter we will study the complete set of eigenfunctions of the Frobenius-Perron operator. To do this we will need an important result from functional analysis ([Ionescu-Tulcea and Marinescu, 1950]).

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Properties of Absolutely Continuous Invariant Measures,val. Chapter 7 gave information on how a transformation decomposes the underlying space into sets each of which supports an acim. In this chapter we present properties of the absolutely continuous invariant measures themselves by studying the densities of these measures.

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