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Measures with positive Lyapunov exponent and conformal measures in rational dynamics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
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
Abstract [en]

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.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-96720DOI: 10.1090/S0002-9947-2012-05366-9ISI: 000303972200001Scopus ID: 2-s2.0-84857667080OAI: oai:DiVA.org:kth-96720DiVA: diva2:532904
Funder
Knut and Alice Wallenberg Foundation
Note
QC 20120612Available from: 2012-06-12 Created: 2012-06-11 Last updated: 2017-12-07Bibliographically approved

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