{"paper":{"title":"Limit cycles for two classes of control piecewise linear differential systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"C.A.B. Rodrigues, J. Llibre, R.D.S. Oliveira","submitted_at":"2018-04-22T21:41:08Z","abstract_excerpt":"We study the bifurcation of limit cycles from the periodic orbits of $2n$--dimensional linear centers $\\dot{x} = A_0 x$ when they are perturbed inside classes of continuous and discontinuous piecewise linear differential systems of control theory of the form $\\dot{x} = A_0 x + \\varepsilon  \\big(A x + \\phi(x_1) b\\big)$, where $\\phi$ is a continuous or discontinuous piecewise linear function, $A_0$ is a $2n\\times 2n$ matrix with only purely imaginary eigenvalues, $\\varepsilon$ is a small parameter, $A$ is an arbitrary $2n\\times 2n$ matrix, and $b$ is an arbitrary vector of $\\mathbb{R}^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08179","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"}