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<p>In this paper, we consider the chaotic dynamics and variational structures of area-preserving maps. There has been extensive research on the dynamics of such maps, and the works of Poincaré and Birkhoff are well known. To explore the variational structures of the area-preserving maps, we define a special class called <i>monotone twist maps</i>. The variational structures derived from the twist maps can be used to construct characteristic trajectories of these maps. Our goal is to prove the existence of an <i>infinite transition orbit</i>, which represents an orbit that oscillates infinitely between two fixed points, using minimizing methods.</p>

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Variational structures for infinite transition orbits of monotone twist maps

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • Yuika Kajihara

摘要

In this paper, we consider the chaotic dynamics and variational structures of area-preserving maps. There has been extensive research on the dynamics of such maps, and the works of Poincaré and Birkhoff are well known. To explore the variational structures of the area-preserving maps, we define a special class called monotone twist maps. The variational structures derived from the twist maps can be used to construct characteristic trajectories of these maps. Our goal is to prove the existence of an infinite transition orbit, which represents an orbit that oscillates infinitely between two fixed points, using minimizing methods.