{"paper":{"title":"Variational principle for weighted topological pressure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"De-Jun Feng, Wen Huang","submitted_at":"2014-11-29T07:15:26Z","abstract_excerpt":"Let $\\pi:X\\to Y$ be a factor map, where $(X,T)$ and $(Y,S)$ are topological dynamical systems. Let ${\\bf a}=(a_1,a_2)\\in {\\Bbb R}^2$ with $a_1>0$ and $a_2\\geq 0$, and $f\\in C(X)$. The ${\\bf a}$-weighted topological pressure of $f$, denoted by $P^{\\bf a}(X, f)$, is defined by resembling the Hausdorff dimension of subsets of self-affine carpets. We prove the following variational principle: $$ P^{\\bf a}(X, f)=\\sup\\left\\{a_1h_\\mu(T)+a_2h_{\\mu\\circ\\pi^{-1}}(S)+\\int f \\;d\\mu\\right\\}, $$ where the supremum is taken over the $T$-invariant measures on $X$. It not only generalizes the variational princ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0078","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"}