Grigoriev R. O., Cross M. C.
Condensed Matter Physics 114-36, California Institute of Technology, Pasadena, California 91125.
Chaos. 1997 Jun;7(2):311-330. doi: 10.1063/1.166222.
A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure of the phase diagram is robust with respect to mild violations of the conservation law. Critical exponents possibly determining a new universality class are calculated for a set of independent order parameters. Numerical evidence is produced suggesting that the singularity in the density of Lyapunov exponents at lambda=0 is a reflection of the singularity in the density of Fourier modes (a "Van Hove" singularity) and disappears if the conservation law is broken. Applicability of the Lyapunov dimension to the description of spatiotemporal chaos in a system with a conservation law is discussed. (c) 1997 American Institute of Physics.
研究了一类属于广泛耦合映射且遵循局部守恒定律的特别简单的模型。确定了系统的相结构和相变类型。有人认为，相图结构对于守恒定律的轻微违反具有鲁棒性。针对一组独立序参量计算了可能决定一个新普适类的临界指数。给出了数值证据，表明在λ = 0处李雅普诺夫指数密度的奇异性是傅里叶模式密度奇异性（“范霍夫”奇异性）的反映，并且如果守恒定律被打破则该奇异性消失。讨论了李雅普诺夫维数在具有守恒定律的系统中对时空混沌描述的适用性。(c) 1997美国物理研究所。
