{"paper":{"title":"Surgery for partially hyperbolic dynamical systems I. Blow-ups of invariant submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrey Gogolev","submitted_at":"2016-09-19T20:14:00Z","abstract_excerpt":"We suggest a method to construct new examples of partially hyperbolic diffeomorphisms. We begin with a partially hyperbolic diffeomorphism $f\\colon M\\to M$ which leaves invariant a submanifold $N\\subset M$. We assume that $N$ is an Anosov submanifold for $f$, that is, the restriction $f|_N$ is an Anosov diffeomorphism and the center distribution is transverse to $TN\\subset TM$. By replacing each point in $N$ with the projective space (real or complex) of lines normal to $N$ we obtain the blow-up $\\hat M$. Replacing $M$ with $\\hat M$ amounts to a surgery on the neighborhood of $N$ which alters "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05925","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"}