コロキウム

We present a rigorous dynamical systems analysis of tubular origami tessellations by identifying the inverse module number, $N^{-1}$, as a perturbation parameter within the framework of Kolmogorov-Arnold-Moser (KAM) theory. In the large-module limit ($N \to \infty$), we prove that the conservative dynamics converges to an integrable map endowed with a variational structure, whose generating function is identified with the total discrete mean curvature. This theoretical result is numerically corroborated by the observation that the phase space is densely populated by invariant curves. By adjusting the mountain-valley fold assignments, we further demonstrate that the system can be transformed into a non-twist map. This adjustment breaks the twist condition, inducing reconnection phenomena and leading to the emergence of novel stable foldable regions in phase space, appearing as elliptic islands. These regions enable the design of foldable configurations that are inaccessible within standard twist regimes. Finally, we analyze the expanding and contracting dynamics of the origami structure within the framework of conformally symplectic systems. By introducing a virtual auxiliary fold that generates a controllable drift term, we numerically confirm the existence of stable quasi-periodic attractors.