Abstract: We define a class of full branch maps with two branches and two neutral fixed points as well as critical points and/or singularities. We construct a Young tower and prove the existence of a sigma-finite invariant measure equivalent to Lebesgue. We also give some necessary and sufficient conditions on the orders of the neutral fixed points and critical points/singularities which imply the existence of a finite invariant measure equivalent to Lebesgue. We prove various statistical properties including decay of correlation and limit theorems. Our class of maps includes pretty much all full branch maps with two orientation preserving branches which have been studied in the literature and we provide a uniform strategy and framework for studying their ergodic properties. This is joint work with Douglas Coates and Mubarak Muhammad.
Doubly Intermittent full branch maps with critical points and singularities
07.04.2022 15:00 - 16:00
Organiser:
H. Bruin, R. Zweimüller
Location: