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The system can be finite- or infinite-dimensional (and quasilinear) and have a non-constant symplectic structure. We allow the origin to be a \u2018trivial\u2019 eigenvalue arising from a translational symmetry or, in an infinite-dimensional setting, to lie in the continuous spectrum of the linearised Hamiltonian vector field provided a compatibility condition on its range is satisfied. As an application, we show how Kirchg\u00e4ssner\u2019s spatial dynamics approach can be used to construct doubly periodic travelling waves on the surface of a three-dimensional body of water (of finite or infinite depth) beneath a thin ice sheet (\u2018hydroelastic waves\u2019). The hydrodynamic problem is formulated as a reversible Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable, and the infinite-dimensional phase space consists of wave profiles which are periodic (with fixed period) in a second, different horizontal direction. Applying our Lyapunov centre theorem at a point in parameter space associated with a 1\u00a0:\u00a01 or <jats:inline-formula><jats:alternatives><jats:tex-math>$$1:-1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>:<\/mml:mo>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> semisimple resonance yields a periodic solution of the spatial Hamiltonian system corresponding to a doubly periodic hydroelastic wave.<\/jats:p>","DOI":"10.1007\/s00332-024-10073-z","type":"journal-article","created":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T01:02:12Z","timestamp":1726275732000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves"],"prefix":"10.1007","volume":"34","author":[{"given":"R.","family":"Ahmad","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. 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