One-Parameter Families of Hyperbolic Iterated Function Systems on the Line - Lecture 3

Explore a detailed lecture on one-parameter families of hyperbolic iterated function systems (IFS) on the line, focusing on an innovative extension of the transversality method. Delve into the study of self-similar measures' dimensions and absolute continuity in hyperbolic IFS contexts, examining how strictly contracting smooth self-mappings operate on compact intervals. Learn about the significance of cylinder separation, pressure formula applications for attractor dimension calculation, and the crucial role of transversality conditions in one-parameter families. Master the advanced technique developed with Bárány, Solomyak, and Śpiewak that enables analysis of parameter-dependent measures and their natural projections. Discover practical applications including the study of Gibbs measures with Hölder continuous potentials, place-dependent Bernoulli convolutions, and Blackwell measure for binary channel, all presented through the lens of cutting-edge research in dynamical systems.