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Invariant densities for C¹ maps

Anthony Quas (1996)

Studia Mathematica

We consider the set of C 1 expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of C 1 expanding maps with the C 1 topology. This is in contrast with results for C 2 or C 1 + ε maps, where the invariant densities can be shown to be continuous.

On a shadowing lemma in metric spaces

Tibor Žáčik (1992)

Mathematica Bohemica

In the present paper conditions are studied, under which a pseudo-orbit of a continuous map f : M → M , where M is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map f .

Currently displaying 61 – 80 of 157