Geometric and Probabilistic Structures in Dynamics
Keith Burns, Dmitry Dolgopyat, Yakov Borisovich Pesin · Contemporary mathematics - American Mathematical Society · 2008
We construct examples of topologically conjugate unimodal maps, such that both of them have an absolutely continuous invariant measure, but for one of them that measure is finite, and for another one it is σ-finite and infinite on every interval.The work is based on the results of Al-Khal, Bruin and Jakobson [2].