{"paper":{"title":"Duality results for Iterated Function Systems with a general family of branches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OC"],"primary_cat":"math.DS","authors_text":"Elismar R. Oliveira, Jairo K. Mengue","submitted_at":"2014-04-30T17:04:42Z","abstract_excerpt":"For $X$, $Y$, $Z$ and $W$ compact metric spaces, consider two uniformly contractive IFS $\\{\\tau_x: Z\\to Z,\\, x\\in x\\}$ and $\\{\\tau_y:W\\to W,\\, y\\in Y\\}$. For a fixed $\\alpha \\in \\mathcal{P}(X)$ with $supp(\\alpha)=X$ we define the entropy of a holonomic measure $\\pi \\in \\mathcal{P}(X\\times Z)$ relative to $\\alpha$, the pressure of a continuous cost function $c(x,z)$ and show that for $c$ Lipschitz this pressure coincides with the spectral radius of the associated transfer operator. The same approach can be applied to the pair $Y,W$. For fixed probabilities $\\alpha \\in \\mathcal{P}(X)$ and $\\beta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7801","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}