{"paper":{"title":"The \"spectral\" decomposition for one-dimensional maps","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexander M. Blokh","submitted_at":"1991-07-27T00:00:00Z","abstract_excerpt":"We construct the \"spectral\" decomposition of the sets $\\bar{Per\\,f}$, $\\omega(f)=\\cup\\omega(x)$ and $\\Omega(f)$ for a continuous map $f$ of the interval to itself. Several corollaries are obtained; the main ones describe the generic properties of $f$-invariant measures, the structure of the set $\\Omega(f)\\setminus \\bar{Per\\,f}$ and the generic limit behavior of an orbit for maps without wandering intervals. The \"spectral\" decomposition for piecewise-monotone maps is deduced from the Decomposition Theorem. Finally we explain how to extend the results of the present paper for a continuous map of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201290","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"}