论文标题
拓扑同步还是简单的吸引子？
Topological synchronisation or a simple attractor?
论文作者
论文摘要
最近的一些论文介绍了拓扑同步的概念。我们特别指的是\ cite {ts}，其中通过偏斜的产品系统说明了该理论，并耦合了两个逻辑图。在这种情况下，我们表明拓扑同步可以很容易地解释为吸引子的诞生，以提高耦合强度的值和两种边缘经验措施的相互收敛性。基于对Lyapunov指数的仔细分析的数值计算表明，吸引子支持绝对连续的物理度量（ACPM）。我们最终表明，对于一些单峰地图，此类ACPM表现出多重分子结构。
A few recent papers introduced the concept of topological synchronisation. We refer in particular to \cite{TS}, where the theory was illustrated by means of a skew product system, coupling two logistic maps. In this case, we show that the topological synchronisation could be easily explained as the birth of an attractor for increasing values of the coupling strength and the mutual convergence of two marginal empirical measures. Numerical computations based on a careful analysis of the Lyapunov exponents suggest that the attractor supports an absolutely continuous physical measure (acpm). We finally show that for some unimodal maps such acpm exhibit a multifractal structure.
