Measures with positive Lyapunov exponent and conformal measures in rational dynamics
2012 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 364, no 6, 2803-2824 p.Article in journal (Refereed) Published
Ergodic properties of rational maps are studied, generalising the work of F. Ledrappier. A new construction allows for simpler proofs of stronger results. Very general conformal measures are considered. Equivalent conditions are given for an ergodic invariant probability measure with positive Lyapunov exponent to be absolutely continuous with respect to a general conformal measure. If they hold, we can construct an induced expanding Markov map with integrable return time which generates the invariant measure.
Place, publisher, year, edition, pages
2012. Vol. 364, no 6, 2803-2824 p.
IdentifiersURN: urn:nbn:se:kth:diva-96720DOI: 10.1090/S0002-9947-2012-05366-9ISI: 000303972200001ScopusID: 2-s2.0-84857667080OAI: oai:DiVA.org:kth-96720DiVA: diva2:532904
FunderKnut and Alice Wallenberg Foundation
QC 201206122012-06-122012-06-112012-06-12Bibliographically approved