Teichmüller space for iterated function systems
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Hille, Martial R.; Snigireva, Nina
Description
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.author | Hille, Martial R. | |
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dc.contributor.author | Snigireva, Nina | |
dc.date.accessioned | 2016-03-11T04:39:21Z | |
dc.date.available | 2016-03-11T04:39:21Z | |
dc.identifier.issn | 1088-4173 | |
dc.identifier.uri | http://hdl.handle.net/1885/100229 | |
dc.description.abstract | 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 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.publisher | American Mathematical Society | |
dc.rights | © 2012 American Mathematical Society | |
dc.source | Conformal Geometry and Dynamics of the American Mathematical Society | |
dc.subject | Iterated function systems | |
dc.subject | inhomogeneous iterated function systems | |
dc.subject | conformal iterated function systems | |
dc.subject | Teichmüller space | |
dc.subject | Hausdorff dimension | |
dc.subject | λ-topology | |
dc.title | Teichmüller space for iterated function systems | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 16 | |
dc.date.issued | 2012 | |
local.identifier.absfor | 010109 | |
local.identifier.ariespublication | f5625xPUB1620 | |
local.publisher.url | http://www.ams.org/journals/ | |
local.type.status | Published Version | |
local.contributor.affiliation | Hille, Martial R, Humboldt University of Berlin, Germany | |
local.contributor.affiliation | Snigireva, Nina, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Department of Mathematics, The Australian National University | |
local.bibliographicCitation.issue | 8 | |
local.bibliographicCitation.startpage | 132 | |
local.bibliographicCitation.lastpage | 160 | |
local.identifier.doi | 10.1090/S1088-4173-2012-00241-X | |
local.identifier.absseo | 970101 | |
dc.date.updated | 2016-06-14T08:35:29Z | |
local.identifier.scopusID | 2-s2.0-84865097942 | |
Collections | ANU Research Publications |
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