{"paper":{"title":"Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eric Bedford, John Smillie, Mikhail Lyubich","submitted_at":"1992-05-28T00:00:00Z","abstract_excerpt":"This paper concerns the dynamics of polynomial automorphisms of ${\\bf C}^2$. One can associate to such an automorphism two currents $\\mu^\\pm$ and the equilibrium measure $\\mu=\\mu^+\\wedge\\mu^-$. In this paper we study some geometric and dynamical properties of these objects. First, we characterize $\\mu$ as the unique measure of maximal entropy. Then we show that the measure $\\mu$ has a local product structure and that the currents $\\mu^\\pm$ have a laminar structure. This allows us to deduce information about periodic points and heteroclinic intersections. For example, we prove that the support "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9205210","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"}