Some characteristics of scaling invariance are discussed for a transition from integrability to non-integrability in a class of dynamical systems described by a two-dimensional, nonlinear and area-preserving mapping. The dynamical variables are action I and angle θ and that the angle diverges in the limit of vanishingly action. The transition is controlled by a parameter ϵ closely related to the order parameter. A scaling invariance observed for the average squared action along the chaotic sea gives evidence that the transition observed from integrability to non-integrability is equivalent to a second-order, also called continuous, phase transition since when the order parameter approaches zero at the same time the response of the order parameter to the conjugate field (susceptibility) diverges. This investigation allows application to a wide class of systems and transitions, including transition from limited to unlimited chaotic diffusion in dissipative sys...

中文翻译：

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混沌系统中连续相变的表征

讨论了在二维，非线性和保留区域映射所描述的一类动力学系统中，从不可积性到不可积性过渡的定标不变性的一些特征。动态变量是作用I和角度θ，该角度在作用消失的极限内发散。过渡由与顺序参数密切相关的参数controlled控制。沿着混沌海域的平方均值观察到的比例不变性表明，从可积性到不可积性的过渡等效于二阶（也称为连续相变），因为当阶次参数同时接近零时阶数参数对共轭场（磁化率）的响应不同。