On invariant measures for piecewise convex transformations
M. Jabłoński (1976)
Annales Polonici Mathematici
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M. Jabłoński (1976)
Annales Polonici Mathematici
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Giulio Pianigiani (1981)
Annales Polonici Mathematici
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Antoni Leon Dawidowicz (1990)
Annales Polonici Mathematici
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Christopher Bose, Véronique Maume-Deschamps, Bernard Schmitt, S. Sujin Shin (2002)
Studia Mathematica
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We investigate the existence and ergodic properties of absolutely continuous invariant measures for a class of piecewise monotone and convex self-maps of the unit interval. Our assumption entails a type of average convexity which strictly generalizes the case of individual branches being convex, as investigated by Lasota and Yorke (1982). Along with existence, we identify tractable conditions for the invariant measure to be unique and such that the system has exponential decay of correlations...
Paweł Góra (1989)
Banach Center Publications
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E. J. Wilezynski (1923)
Journal de Mathématiques Pures et Appliquées
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F. Schweiger (1989)
Banach Center Publications
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Franz Hofbauer (1988)
Monatshefte für Mathematik
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H. Gacki, A. Lasota, J. Myjak (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show upper estimates of the concentration and thin dimensions of measures invariant with respect to families of transformations. These estimates are proved under the assumption that the transformations have a squeezing property which is more general than the Lipschitz condition. These results are in the spirit of a paper by A. Lasota and J. Traple [Chaos Solitons Fractals 28 (2006)] and generalize the classical Moran formula.
M. Jabłoński, J. Malczak (1984)
Colloquium Mathematicae
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Massimo Campanino, Stefano Isola (1996)
Forum mathematicum
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Adl-Zarabi, Kourosh, Proppe, Harald (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Jan Mycielski (1974)
Colloquium Mathematicae
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Andrzej Pelc
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CONTENTS0. Introduction...........................................51. Preliminaries.........................................72. Universal invariant measures..............133. Extensions of invariant measures........214. Saturation of ideals on groups............34References.............................................46
K. Krzyżewski (1979)
Colloquium Mathematicae
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Francesc Bofill (1988)
Stochastica
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The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mu for each parameter value b. The continuity of the map b --> mu is established.