On singularly perturbed ordinary differential equations with measure-valued limits
Artstein, Zvi
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Artstein, Zvi
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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.
Piotr Zakrzewski (1997)
Colloquium Mathematicae
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Let G be a group of homeomorphisms of a nondiscrete, locally compact, σ-compact topological space X and suppose that a Haar measure on X exists: a regular Borel measure μ, positive on nonempty open sets, finite on compact sets and invariant under the homeomorphisms from G. Under some mild assumptions on G and X we prove that the measure completion of μ is the unique, up to a constant factor, nonzero, σ-finite, G-invariant measure defined on its domain iff μ is ergodic and the G-orbits...
Pavol Brunovský, Jozef Komorník (1986)
Časopis pro pěstování matematiky
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van Gaans, Onno, van Neerven, Jan (2006)
Electronic Communications in Probability [electronic only]
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