非测地双曲发电机中的磁场反转和拓扑熵
Magnetic field reversals and topological entropy in non-geodesic hyperbolic dynamos
摘要：
在此之前，Chicone，Latushkin和Montgomery-Smith [Comm Math Phys（1997）]已经证明了在紧致二维流形中，只要其黎曼曲率为常数且为负，则存在一个快速发电机算子.最近，Gallet和Petrelis [Phys Rev \textbf{E}，80（2009）]研究了湍流发电机中的鞍结分叉，作为磁场反转的模型。由于鞍节点创建的双曲流，这为我们提供了物理动机，调查这些逆转在一个简单的运动发电机模型从一个力自由的非测地线稳定流在罗巴切夫斯基平面。在扩散作用下，磁矢势在一个方向上增长，在另一个方向上衰减。磁场微分2-形式是正交于平面。还给出了双曲空间中的一个恢复强迫发电机。磁场反转从这个模型中获得。还计算了拓扑熵[Klapper和Young，Comm Math Phys（1995）]。
英文摘要：
Earlier, Chicone, Latushkin and Montgomery-Smith [Comm Math Phys (1997)] have proved the existence of a fast dynamo operator, in compact two-dimensional manifold, as long as its Riemannian curvature be constant and negative. More recently Gallet and Petrelis [Phys Rev \textbf{E}, 80 (2009)] have investigated saddle-node bifurcation, in turbulent dynamos as modelling for magnetic field reversals. Since saddle nodes are created in hyperbolic flows, this provides us with physical motivation to investigate these reversals in a simple kinematic dynamo model obtained from a force-free non-geodesic steady flow in Lobachevsky plane. Magnetic vector potential grows in one direction and decays in the other under diffusion. Magnetic field differential 2-form is orthogonal to the plane. A restoring forcing dynamo in hyperbolic space is also given. Magnetic field reversals are obtained from this model. Topological entropies [Klapper and Young, Comm Math Phys (1995)] are also computed.
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