{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:26:19Z","timestamp":1787232379268,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We consider a two-dimensional piecewise-smooth system defined in two domains separated by a switching manifold $\\Sigma$. We assume that there exists a piecewise-defined continuous Hamiltonian that is a first integral of the system. We also suppose that the system possesses an invisible fold-fold at the origin and two heteroclinic orbits connecting two hyperbolic critical points on either side of $\\Sigma$. Finally, we assume that the region enclosed by these heteroclinic connections is fully covered by periodic orbits surrounding the origin, whose periods monotonically increase as they approach the heteroclinic connection. For a nonautonomous ($T$-periodic) Hamiltonian perturbation of amplitude $\\varepsilon$, we rigorously prove, for every $n$ and $m$ relatively prime and $\\varepsilon&gt;0$ small enough, that there exists an $nT$-periodic orbit impacting $2m$ times with the switching manifold at every period if a modified subharmonic Melnikov function possesses a simple zero. We also prove that if the orbits are discontinuous when they cross $\\Sigma$, then all these orbits exist if the relative size of $\\varepsilon&gt;0$ with respect to the magnitude of this jump is large enough. In addition, we obtain similar conditions for the splitting of the heteroclinic connections.<\/jats:p>","DOI":"10.1137\/110850359","type":"journal-article","created":{"date-parts":[[2012,7,10]],"date-time":"2012-07-10T16:59:59Z","timestamp":1341939599000},"page":"801-830","source":"Crossref","is-referenced-by-count":48,"title":["The Melnikov Method and Subharmonic Orbits in a Piecewise-Smooth System"],"prefix":"10.1137","volume":"11","author":[{"given":"A.","family":"Granados","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S. J.","family":"Hogan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T. M.","family":"Seara","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,7,10]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-007-9087-9"},{"key":"atypb2","unstructured":"F. Battelli and M. Fec\u030ckan,\n                      Nonsmooth homoclinic orbits, Melnikov functions and chaos in discontinuous systems\n                      , Phys. 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