Artículos de revistas
Structure of distributions generated by the scenery flow
Fecha
2015-01Registro en:
Käenmäki, Antti; Sahlsten, Tuomas; Shmerkin, Pablo Sebastian; Structure of distributions generated by the scenery flow; Wiley; Journal Of The London Mathematical Society-second Series; 91; 2; 1-2015; 464-494
0024-6107
CONICET Digital
CONICET
Autor
Käenmäki, Antti
Sahlsten, Tuomas
Shmerkin, Pablo Sebastian
Resumen
We expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution (FD) in the sense of Hochman is generated by a USM, which provides a converse to a regularity theorem on the structure of distributions generated by the scenery flow. We further show that the collection of FDs is closed under the weak topology and, moreover, is a Poulsen simplex, that is, extremal points are dense. We apply these to show that a Baire generic measure is as far as possible from being uniformly scaling: at almost all points, it has all FDs as tangent distributions.