{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:32:38Z","timestamp":1787506358315,"version":"build-2736575974"},"reference-count":3,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[1993,3]]},"abstract":"<jats:p>For the class of periodic functions $u(x)$ that can be associated with closed orbits in the $(u,u')$ phase-plane described by a differential equation of the form $u'^2 = p - F(u)$, around some local minimum of $F(u)$, a useful integral expression is obtained for any derivative with respect to the parameter p of any suitably differentiable function of u and p integrated over one period in x. That is, an expression is found for $({d}\/{dp})^k \\int_0^{\\lambda (p)} {f(u,p)dx} $, where $\\lambda (p)$ is the period. Some illustrative examples are presented concerning relationships between moments of $u(x)$ and some forms of the function $F(u)$.<\/jats:p>","DOI":"10.1137\/1035007","type":"journal-article","created":{"date-parts":[[2005,3,7]],"date-time":"2005-03-07T02:32:15Z","timestamp":1110162735000},"page":"125-129","source":"Crossref","is-referenced-by-count":1,"title":["A Note on Integral Properties of Periodic Orbits"],"prefix":"10.1137","volume":"35","author":[{"given":"J. W.","family":"Dold","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","volume-title":"Nonlinear ordinary differential equations","author":"Jordan D. W.","year":"1987"},{"key":"R2","volume-title":"Applied mathematics","author":"Logan J. David","year":"1987"},{"key":"R3","volume-title":"Nonlinear dynamics and chaos","author":"Thompson J. M. T.","year":"1986"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/1035007","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:40:08Z","timestamp":1787236808000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/1035007"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,3]]},"references-count":3,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,3]]}},"alternative-id":["10.1137\/1035007"],"URL":"https:\/\/doi.org\/10.1137\/1035007","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,3]]}}}