6533b870fe1ef96bd12d0794
RESEARCH PRODUCT
Structure of distributions generated by the scenery flow
Pablo ShmerkinAntti KäenmäkiTuomas Sahlstensubject
Dynamical systems theoryWeak topologyMatemáticasGeneral MathematicsdistributionsDynamical Systems (math.DS)Scenery flowMeasure (mathematics)Matemática PuraFractalPrimary 37A10 28A80 Secondary 28A33 28A75Fractal distributionClassical Analysis and ODEs (math.CA)FOS: MathematicsErgodic theoryscenery flowMathematics - Dynamical SystemsScalingMathematicsCP-processergodic theoryMathematical analysista111Distribution (mathematics)Flow (mathematics)Mathematics - Classical Analysis and ODEsCIENCIAS NATURALES Y EXACTASdescription
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 in the sense of Hochman is generated by a uniformly scaling measure, 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 fractal distributions 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 fractal distributions as tangent distributions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-09 |