{"paper":{"title":"On the dynamics of a rational semigroup on a convolution measure algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. T. Baraviera, E. R. Oliveira, F. B. Rodrigues","submitted_at":"2014-11-15T19:12:40Z","abstract_excerpt":"We are going to study the dynamical properties of the rational semigroup $Q_{t}(\\mu)$ where $Q_{t}(\\mu)= (1-t) \\mu * (1- t \\mu)^{-1},$ for $t \\in [0,1)$, that is defined for $\\mu \\in \\mathcal{P}(G)$, the set of Borel probabilities over $(G, \\cdot)$ an abelian compact topological group where we define the \\textbf{convolution}, $\\nu * \\mu \\in \\mathcal{P}(G)$, as usual for a group $\\int f d(\\nu * \\mu)= \\int \\int f(xy) d\\nu(x) d\\mu(y),$ then $(\\mathcal{P}(G), *)$ became a $\\textbf{convolution measure algebra}$ (CM-algebra). We investigate several properties for this semigroup (as the Stable Manifo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4177","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":""},"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"}