In this work, we show that the bailout embedding method is responsible for creating different dynamical behaviors and for destroying intrinsic features present in mixed phase spaces of the area-preserving Hamiltonian maps, where the sticking to regular (or resonant) islands degrades chaotic properties. In particular, the base map chosen for the study is the two-dimensional (2D) Web Map (WM). The four-dimensional (4D) embedded Web Map dynamics is governed by four-parameters: ([Formula: see text]) in the WM control the nonlinearity and the type of symmetry structures (crystalline or quasi-crystalline) in phase space, respectively; ([Formula: see text]) in the embedding equations determine the mass density ratio and dissipation, respectively. For specific parameter combinations we explore the existence of transient chaos phenomenon, hyperchaotic dynamics and control the degradation of the underlying diffusive behaviors observed in phase space of the WM. If the WM is subjected to large enough dissipation through the embedding equations, stable periodic points (inside resonance islands) become sinks attracting almost all the surrounding orbits, destroying all invariant curves which divide the phase space into chaotic and regular domains. As area-preserving maps obtained from Hamiltonian flows usually share the crucial property that resonance islands can be found immersed in chaotic sea (characterizing the mixed phase space) for appropriated parameter combinations, the results obtained here for the 4D embedded WM should be considered generic for such whole class of nonlinear systems.

中文翻译：

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救助嵌入 Web 地图中的瞬态混沌、超混沌动力学和传输特性

在这项工作中，我们表明救助嵌入方法负责创建不同的动力学行为并破坏存在于区域保持哈密顿图的混合相空间中的内在特征，其中坚持规则（或共振）岛会降低混沌特性。特别是，为研究选择的底图是二维 (2D) Web 地图 (WM)。四维 (4D) 嵌入式 Web 地图动力学由四个参数控制：（[公式：见文本]）在 WM 中分别控制相空间中的非线性和对称结构（晶体或准晶体）的类型; 嵌入方程中的（[公式：见正文]）分别确定质量密度比和耗散。对于具体的参数组合我们探讨了瞬态混沌现象的存在，超混沌动力学并控制在 WM 相空间中观察到的潜在扩散行为的退化。如果 WM 通过嵌入方程受到足够大的耗散，则稳定的周期点（在共振岛内）变成吸引几乎所有周围轨道的汇，破坏所有将相空间划分为混沌和规则域的不变曲线。由于从哈密顿流中获得的面积保持图通常具有这样的关键特性，即可以在混沌海中找到共振岛（表征混合相空间）以进行适当的参数组合，因此此处获得的 4D 嵌入式 WM 的结果应该被认为是通用的这样一整类非线性系统。