Dynamics seminar: Adam Śpiewak (BIU) Parameter dependent invariant measures for iterated function systems - dimension and absolute continuity

Tue, 02/11/202114:00-15:00
Abstract: Consider a one-parameter family of iterated function systems on the interval and a family of measures on the corresponding symbolic space, depending on the same parameter. We study geometric properties of measures projected by the natural projection corresponding to the IFS.  Assuming that IFS satisfies a transversality condition and measures depend on the parameter regularly enough, we obtain results on the value of the dimension and absolute continuity of the projected measure for almost every parameter. This extends classical results for projections of a fixed measure in the symbolic space and applies e.g. to invariant measures for systems with place-dependent probabilities and equilibrium measures for hyperbolic iterated function systems. The talk is based on a recent joint work with Balázs Bárány, Károly Simon and Boris Solomyak.

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Meeting ID: 835 6502 3896
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