On essentially absolutely continuous plane transformations

On Essentially Absolutely Continuous Plane Transformations

On Absolutely Continuous Transformations

NONINVERTIBLE TRANSFORMATIONS ADMITTING NO ABSOLUTELY CONTINUOUS ct-FINITE INVARIANT MEASURE

We study a family of H-to-1 conservative ergodic endomorphisms which we will show to admit no rj-finite absolutely continuous invariant measure. We exhibit recurrent measures for these transformations and study their ratio sets; the examples can be realized as C°° endomorphisms of the 2-torus.

Absolutely Continuous, Invariant Measures for Dissipative, Ergodic Transformations

We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these. Introduction Let (X,B, m, T ) be an invertible, ergodic measure preserving transformation of a σ-finite measure space, then there are no other σ-finite, m-absolu...

Absolutely continuous invariant measures for piecewise real-analytic expanding maps on the plane

We prove the existence of absolutely continuous invariant measures for piecewise real-analytic expanding maps on bounded regions in the plane.