{"paper":{"title":"Ruelle Operator for Infinite Conformal IFS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Li-Yan Wu, Xiao-Peng Chen, Yuan-Ling Ye","submitted_at":"2009-04-07T15:23:26Z","abstract_excerpt":"Let $(X, \\{w_j \\}_{j=1}^m, \\{p_j \\}_{j=1}^m)$ ($2 \\leq m < \\infty$) be a contractive iterated function system (IFS), where $X$ is a compact subset of ${\\Bbb{R}}^d$. It is well known that there exists a unique nonempty compact set $K$ such that $K=\\bigcup_{j=1}^m w_j(K)$. Moreover, the Ruelle operator on $C(K)$ determined by the IFS $(X, \\{w_j \\}_{j=1}^m, \\{p_j \\}_{j=1}^m)$ ($2 \\leq m < \\infty$) has been introduced in \\cite{FL}. In the present paper, the Ruelle operators determined by the infinite conformal IFSs are discussed. Some separation properties for the infinite conformal IFSs are inves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1164","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0904.1164/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}