Leírás
(Joint result with Balázs Bárány, Boris Solomyak and Adam Spiewak.)
We consider one-parameter families of smooth uniformly contractive (not necessarily self-similar) iterated function systems on the real line, which smoothly depend on the parameter. We always assume that the families under consideration satisfy a technical condition called the transversality condition.
One of the most important families of dynamically defined measures is the Gibbs measures for the potentials corresponding to the logarithm of the derivatives.
Our main result says that these Gibbs measures are absolutely continuous with respect to the Lebesgue measure for almost all parameters such that the ratio of the entropy and Lyapunov exponent is larger than 1. Besides this, some other consequences of our results will be stated in the talk, preceded by a sufficient introduction to the topic.
The talk is online.
Zoom link: https://zoom.us/j/93746696898?pwd=b1J2MnEwMVdDVElPUFRkYWdtVXdWdz09
Meeting ID: 937 4669 6898
Passcode: 280561