Invariant measures and ergodic properties of number theoretical endomorphisms
F. Schweiger (1989)
Banach Center Publications
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F. Schweiger (1989)
Banach Center Publications
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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...
Giulio Pianigiani (1981)
Annales Polonici Mathematici
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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.
Tomoki Inoue (1992)
Annales Polonici Mathematici
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We study the asymptotic stability of densities for piecewise convex maps with flat bottoms or a neutral fixed point. Our main result is an improvement of Lasota and Yorke's result ([5], Theorem 4).
Anthony Quas (1999)
Studia Mathematica
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We consider the topological category of various subsets of the set of expanding maps from a manifold to itself, and show in particular that a generic expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for or expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.
Góra, P., Boyarsky, A., Lou, Y. S. (1997)
Journal of Applied Mathematics and Stochastic Analysis
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Piotr Bugiel (1996)
Mathematische Zeitschrift
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Das, G., Patel, B.K. (1989)
International Journal of Mathematics and Mathematical Sciences
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Thomas Bogenschütz, Zbigniew Kowalski (1996)
Studia Mathematica
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We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.
Góra, Paweł, Boyarsky, Abraham, Islam, Md.Shafiqul (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Franz Hofbauer, Peter Raith, Thomas Steinberger (2003)
Fundamenta Mathematicae
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The multifractal generalizations of Hausdorff dimension and packing dimension are investigated for an invariant subset A of a piecewise monotonic map on the interval. Formulae for the multifractal dimension of an ergodic invariant measure, the essential multifractal dimension of A, and the multifractal Hausdorff dimension of A are derived.
Maximilian Thaler (2000)
Studia Mathematica
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We determine the asymptotic behaviour of the iterates of the Perron-Frobenius operator for specific interval maps with an indifferent fixed point which gives rise to an infinite invariant measure.
F. Martín-Reyes, A. de la Torre (1994)
Studia Mathematica
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Paweł Góra (1989)
Banach Center Publications
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