{"paper":{"title":"The stability index for dynamically defined Weierstrass functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Charles P Walkden, Tom Withers","submitted_at":"2017-09-07T21:04:17Z","abstract_excerpt":"Let $\\hat{T} : X \\times \\mathbb{R} \\to X \\times \\mathbb{R}$ given by $\\hat{T}(x,t) = (Tx, g_x(t))$ be a skew-product dynamical system where $T : X \\to X$ is a mixing conformal expanding map and, for each $x \\in X$, $g_x : \\mathbb{R} \\to \\mathbb{R}$ is an affine map of the form $g_x(t)=-f(x)+\\lambda(x)^{-1}t$. Under a suitable contraction hypotheses on $\\lambda$ there exists a measurable function $u: X \\to \\mathbb{R}$ such that $\\text{graph}(u) = \\{(x,u(x)) \\mid x\\in X\\}$ is $\\hat{T}$-invariant and divides $X \\times \\mathbb{R}$ into two regions, $\\mathbb{B}^+$ and $\\mathbb{B}^-$, consisting of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02451","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"}