{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:30:56Z","timestamp":1787229056941,"version":"build-2736575974"},"reference-count":49,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>The phase space of an integrable, volume-preserving map with one action and d angles is foliated by a one-parameter family of d-dimensional invariant tori. Perturbations of such a system may lead to chaotic dynamics and transport. We show that near a rank-one, resonant torus these mappings can be reduced to volume-preserving \u201cstandard maps.\u201d These have twist only when the image of the frequency map crosses the resonance curve transversely. We show that these maps can be approximated\u2014using averaging theory\u2014by the usual area-preserving twist or nontwist standard maps. The twist condition appropriate for the volume-preserving setting is shown to be distinct from the nondegeneracy condition used in (volume-preserving) KAM theory.<\/jats:p>","DOI":"10.1137\/110846865","type":"journal-article","created":{"date-parts":[[2012,3,8]],"date-time":"2012-03-08T18:22:05Z","timestamp":1331230925000},"page":"319-349","source":"Crossref","is-referenced-by-count":16,"title":["Resonances and Twist in Volume-Preserving Mappings"],"prefix":"10.1137","volume":"11","author":[{"given":"H. R.","family":"Dullin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. D.","family":"Meiss","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,3,8]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.3139\/217.0125"},{"key":"R2","unstructured":"R. P. Argarwal,\n                      Difference Equations and Inequalities: Theory, Methods and Applications\n                      , Monographs and Textbooks in Pure and Applied Mathematics 228, Marcel Dekker, New York, 2000."},{"key":"R3","unstructured":"A. Bazzani and A. Di Sebastiano,\n                      Perturbation theory for volume-preserving maps: Application to the magnetic field lines in plasma physics\n                      , in Analysis and Modelling of Discrete Dynamical Systems, Adv. Discrete Math. 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