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It is proved that the exact number of limit cycles emerging from the period annulus surrounding"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.01553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-05T02:30:55Z","cross_cats_sorted":[],"title_canon_sha256":"9cfac3bb51ad60f1c9892920ce766999de1b18b50dcd8a6bda87a81fc64eaa78","abstract_canon_sha256":"36681050ea53774744b04783705282b49a464f7d8057918bf71fa570b474e30e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:52.617451Z","signature_b64":"aU3VA4jAB93PfVEFIdfW+rjMKibqw/nRgshO3rHObNLU3xL6fU/qtiw2ulsw6fnUMMQBqVd/CffSNsvMC5lxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c364a8c7c22610f1a9c8ab19e225dfcbbad1f876e3025f25e53f065e49b1f34b","last_reissued_at":"2026-05-18T00:08:52.616674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:52.616674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit cycles appearing from perturbations of cubic piecewise smooth center with double invariant real straight lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jihua Yang, Liqin Zhao","submitted_at":"2018-08-05T02:30:55Z","abstract_excerpt":"This paper investigates the exact number of limit cycles given by the averaging theory of first order for the piecewise smooth integrable non-Hamiltonian system \\begin{eqnarray*} (\\dot{x},\\ \\dot{y})=\\begin{cases} (-y(x+a)^2+\\varepsilon f^+(x,y),\\ x(x+a)^2+\\varepsilon g^+(x,y)),\\ \\ x\\geq0,\\\\ (-y(x+b)^2+\\varepsilon f^-(x,y),\\ x(x+b)^2+\\varepsilon g^-(x,y)),\\ ~ \\, x<0,\\\\ \\end{cases}\\end{eqnarray*} where $ab\\neq 0$, $0<|\\varepsilon|\\ll 1$, and $f^\\pm(x,y)$ and $g^\\pm(x,y)$ are polynomials of degree $n$. 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