Smoothness of invariant density for expanding transformations in higher dimensions.
Adl-Zarabi, Kourosh, Proppe, Harald (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Adl-Zarabi, Kourosh, Proppe, Harald (2000)
Journal of Applied Mathematics and Stochastic Analysis
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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.
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...
F. Schweiger (1989)
Banach Center Publications
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Rao, M.B. (1978)
Portugaliae mathematica
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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.
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.
Michael Lin (2000)
Colloquium Mathematicae
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Let T be a positive linear contraction of of a σ-finite measure space (X,Σ,μ) which overlaps supports. In general, T need not be completely mixing, but it is in the following cases: (i) T is the Frobenius-Perron operator of a non-singular transformation ϕ (in which case complete mixing is equivalent to exactness of ϕ). (ii) T is a Harris recurrent operator. (iii) T is a convolution operator on a compact group. (iv) T is a convolution operator on a LCA group.
Tomasz Nowicki, Sebastian Van Strien (1990)
Annales de l'I.H.P. Physique théorique
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Zbigniew Kowalski (1994)
Applicationes Mathematicae
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We consider the skew product transformation T(x,y)= (f(x), ) where f is an endomorphism of a Lebesgue space (X,A,p), e : X → S and is a family of Lasota-Yorke type maps of the unit interval into itself. We obtain conditions under which the ergodic properties of f imply the same properties for T. Consequently, we get the asymptotical stability of random perturbations of a single Lasota-Yorke type map. We apply this to some probabilistic model of the motion of cogged bits in the rotary...
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.
F. Martín-Reyes, A. de la Torre (1994)
Studia Mathematica
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