Cultural advice

The Australian National University acknowledges, celebrates and pays our respects to the Ngunnawal and Ngambri people of the Canberra region and to all First Nations Australians on whose traditional lands we meet and work, and whose cultures are among the oldest continuing cultures in human history.

Aboriginal and Torres Strait Islander peoples are advised that ANU Library collections may include images, names, voices, and other representations of deceased persons.

Material in the collection may contain terms, language or views that reflect the period in which the item was created and may be considered inappropriate today.

Ambiguity in the Determination of the Free Energy Associated with the Critical Circle Map

Simple item page
dc.contributor.authorKenny, Brian
dc.contributor.authorDixon, Tony
dc.date.accessioned2015-12-07T22:38:38Z
dc.date.issued2008
dc.date.updated2016-02-24T11:05:05Z
dc.description.abstractWe consider a simple model to describe the widths of the mode-locked intervals for the critical circle map. By using two different partitions of the rational numbers based on Farey series and Farey tree levels, respectively, we calculate the free energy analytically at selected points for each partition. It emerges that the result of the calculation depends on the method of partition. An implication of this finding is that the generalized dimensions Dq are different for the two types of partition except when q=0; that is, only the Hausdorff dimension is the same in both cases.
dc.identifier.issn1446-8735
dc.identifier.urihttp://hdl.handle.net/1885/23517
dc.publisherAustralian Mathematical Society
dc.sourceANZIAM Journal
dc.subjectKeywords: circle maps; Farey series; Farey trees; thermodynamic formalism
dc.titleAmbiguity in the Determination of the Free Energy Associated with the Critical Circle Map
dc.typeJournal article
local.bibliographicCitation.lastpage184
local.bibliographicCitation.startpage177
local.contributor.affiliationKenny, Brian, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationDixon, Tony, Curtin University of Technology
local.contributor.authoruidKenny, Brian, t879
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.identifier.absfor010204 - Dynamical Systems in Applications
local.identifier.ariespublicationu4348025xPUB27
local.identifier.citationvolume50
local.identifier.doi10.1017/S1446181108000291
local.identifier.scopusID2-s2.0-77954671155
local.type.statusPublished Version

Downloads

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
01_Kenny_Ambiguity_in_the_Determination_2008.pdf
Size:
117.43 KB
Format:
Adobe Portable Document Format
Download

Collections

ANU Research Publications

DSpace software copyright © 2002-2026 LYRASIS