Jablonski proved that a piecewise expanding C² multidimensional Jablonski map admits an absolutely continuous invariant probability measure (ACIP). Boyarsky and Lou extended this result to the case of i.i.d. compositions of the above maps, with an on average expanding condition. We generalize these results to the (quenched) setting of random Jablonski maps, where the randomness is governed by an ergodic, invertible and measure preserving transformation. We prove that the skew product associated to this random dynamical system admits a finite number of ergodic ACIPs. Furthermore, we provide two different upper bounds on the number of mutually singular ergodic ACIP's, motivated by the works of Buzzi in one dimension and Gora, Boyarsky and Proppe in higher dimensions.

About Applied and computational maths seminars

Our seminars bring together UQ's applied and computational mathematics communities.

UQ and invited scientists deliver the presentations, which are informal and promote discussion.

We welcome suggestions for speakers and topics from staff, students and visitors, and encourage students to share their work.

Our seminars are usually held on Thursdays from 3pm to 4pm.

To suggest a topic or speaker, and for more information, contact Dr Dietmar Oelz or Dr Cecilia Gonzalez Tokman.