论文标题
Heterochaos面包师地图和Dyck系统：最大熵测量和熵易接近性的机制
Heterochaos baker maps and the Dyck system: maximal entropy measures and a mechanism for the breakdown of entropy approachability
论文作者
论文摘要
我们在$ [0,1]^2 $和$ [0,1]^3 $上介绍了两个分段仿射图的参数化家族，作为Heterochaos Baker Maps的概括，这些图是在[Y.中引入和调查的。 Saiki，H。Takahasi，J。A. Yorke，非线性，34（2021），5744--5761]作为多维动力学系统中不稳定尺寸可变性的最小模型。我们表明，这些地图的自然编码空间与来自语言理论的Dyck系统一致。基于这种巧合，我们开始对其不变措施进行互补分析。作为第一次尝试，我们显示了对广义杂色贝克图的最大熵的两种千古测量。我们还阐明了熵易接近性的机制。
We introduce two parametrized families of piecewise affine maps on $[0,1]^2$ and $[0,1]^3$, as generalizations of the heterochaos baker maps which were introduced and investigated in [Y. Saiki, H. Takahasi, J. A. Yorke, Nonlinearity, 34 (2021), 5744--5761] as minimal models of the unstable dimension variability in multidimensional dynamical systems. We show that natural coding spaces of these maps coincide with the Dyck system that has come from the theory of languages. Based on this coincidence, we start to develop a complementary analysis on their invariant measures. As a first attempt, we show the existence of two ergodic measures of maximal entropy for the generalized heterochaos baker maps. We also clarify a mechanism for the breakdown of entropy approachability.
