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Nice sets and invariant densities in complex dynamics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2011 (English)In: Mathematical proceedings of the Cambridge Philosophical Society (Print), ISSN 0305-0041, E-ISSN 1469-8064, Vol. 150, 157-165 p.Article in journal (Refereed) Published
Abstract [en]

In complex dynamics, we construct a so-called nice set (one for which the first return map is Markov) around any point which is in the Julia set but not in the post-singular set, adapting a construction of Rivera-Letelier. This simplifies the study of absolutely continuous invariant measures. We prove a converse to a recent theorem of Kotus and 'Swiatek, so for a certain class of meromorphic maps the absolutely continuous invariant measure is finite if and only if an integrability condition is satisfied.

Place, publisher, year, edition, pages
2011. Vol. 150, 157-165 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-29362DOI: 10.1017/S0305004110000265ISI: 000285474400009Scopus ID: 2-s2.0-79451469273OAI: oai:DiVA.org:kth-29362DiVA: diva2:395144
Funder
EU, European Research Council
Note
QC 20110204Available from: 2011-02-04 Created: 2011-02-01 Last updated: 2017-12-11Bibliographically approved

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