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Teichmüller space for iterated function systems

Hille, Martial R.; Snigireva, Nina

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In this paper we investigate families of iterated function systems (IFS) and conformal iterated function systems (CIFS) from a deformation point of view. Namely, we introduce the notion of Teichm¨uller space for finitely and infinitely generated (C)IFS and study its topological and metric properties. Firstly, we completely classify its boundary. In particular, we prove that this boundary essentially consists of inhomogeneous systems. Secondly, we equip Teichmüller space for (C)IFS with...[Show more]

dc.contributor.authorHille, Martial R.
dc.contributor.authorSnigireva, Nina
dc.date.accessioned2016-03-11T04:39:21Z
dc.date.available2016-03-11T04:39:21Z
dc.identifier.issn1088-4173
dc.identifier.urihttp://hdl.handle.net/1885/100229
dc.description.abstractIn this paper we investigate families of iterated function systems (IFS) and conformal iterated function systems (CIFS) from a deformation point of view. Namely, we introduce the notion of Teichm¨uller space for finitely and infinitely generated (C)IFS and study its topological and metric properties. Firstly, we completely classify its boundary. In particular, we prove that this boundary essentially consists of inhomogeneous systems. Secondly, we equip Teichmüller space for (C)IFS with different metrics, an Euclidean, a hyperbolic, and a λ-metric. We then study continuity of the Hausdorff dimension function and the pressure function with respect to these metrics. We also show that the hyperbolic metric and the λ-metric induce topologies stronger than the non-metrizable λ-topology introduced by Roy and Urbanski and, therefore, provide an alternative to the λ-topology in the study of continuity of the Hausdorff dimension function and the pressure function. Finally, we investigate continuity properties of various limit sets associated with infinitely generated (C)IFS with respect to our metrics.
dc.publisherAmerican Mathematical Society
dc.rights© 2012 American Mathematical Society
dc.sourceConformal Geometry and Dynamics of the American Mathematical Society
dc.subjectIterated function systems
dc.subjectinhomogeneous iterated function systems
dc.subjectconformal iterated function systems
dc.subjectTeichmüller space
dc.subjectHausdorff dimension
dc.subjectλ-topology
dc.titleTeichmüller space for iterated function systems
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume16
dc.date.issued2012
local.identifier.absfor010109
local.identifier.ariespublicationf5625xPUB1620
local.publisher.urlhttp://www.ams.org/journals/
local.type.statusPublished Version
local.contributor.affiliationHille, Martial R, Humboldt University of Berlin, Germany
local.contributor.affiliationSnigireva, Nina, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Department of Mathematics, The Australian National University
local.bibliographicCitation.issue8
local.bibliographicCitation.startpage132
local.bibliographicCitation.lastpage160
local.identifier.doi10.1090/S1088-4173-2012-00241-X
local.identifier.absseo970101
dc.date.updated2016-06-14T08:35:29Z
local.identifier.scopusID2-s2.0-84865097942
CollectionsANU Research Publications

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