Metastability of certain intermittent maps
Metastability of certain intermittent maps
复制标题
某些间歇图的亚稳定性
DOI：
10.1088/0951-7715/25/1/107
复制
发表时间：
2011
期刊：
影响因子：
1.7
通讯作者：
S. Vaienti
中科院分区：
文献类型：
--
作者：
Wael Bahsoun;S. Vaienti
研究了具有两个遍历不变密度的间歇映射。密度由具有公共边界点的两个子区间支持。由于某些扰动，质量通过最初不变的子区间的子集（称为孔）泄漏，并迫使子系统合并成一个具有一个不变密度的系统。我们证明了扰动系统的不变密度在L1-范数下收敛于间歇映射的不变密度的一个特定的凸组合。特别地，我们证明了组合中的权重比等于孔的测度比的极限。
We study an intermittent map which has exactly two ergodic invariant densities. The densities are supported on two subintervals with a common boundary point. Due to certain perturbations, leakage of mass through subsets, called holes, of the initially invariant subintervals occurs and forces the subsystems to merge into one system that has exactly one invariant density. We prove that the invariant density of the perturbed system converges in the L1-norm to a particular convex combination of the invariant densities of the intermittent map. In particular, we show that the ratio of the weights in the combination is equal to the limit of the ratio of the measures of the holes.