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<p>We consider nonlinear reversible beam equations with quasiperiodically forced terms, where the multi-dimensional forcing frequency is beyond the Brjuno condition. We focus our attention on the three equilibria of the unperturbed equation and construct the real analytic small response solutions around them. Moreover, note that the linearized systems around two of the equilibria are hyperbolic–elliptic, then we construct the stable manifolds of quasiperiodic solutions. The main proof is based on a modified infinite-dimensional KAM theorem for reversible systems with partly hyperbolic variables.</p>

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Response Solutions to Reversible Beam Equations Beyond Multi-dimensional Brjuno Frequency and their Stable Manifolds

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Shimin Wang

摘要

We consider nonlinear reversible beam equations with quasiperiodically forced terms, where the multi-dimensional forcing frequency is beyond the Brjuno condition. We focus our attention on the three equilibria of the unperturbed equation and construct the real analytic small response solutions around them. Moreover, note that the linearized systems around two of the equilibria are hyperbolic–elliptic, then we construct the stable manifolds of quasiperiodic solutions. The main proof is based on a modified infinite-dimensional KAM theorem for reversible systems with partly hyperbolic variables.