The rate of convergence of new Lax–Oleinik type operators for time-periodic positive definite Lagrangian systems
The rate of convergence of new Lax–Oleinik type operators for time-periodic positive definite Lagrangian systems
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DOI：
10.1088/0951-7715/25/7/2039
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发表时间：
2011-09
期刊：
影响因子：
1.7
通讯作者：
Kaizhi Wang;Jun Yan
中科院分区：
文献类型：
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作者：
Kaizhi Wang;Jun Yan
假设时间周期正定拉格朗日L的奥布里集由一个双曲1周期轨道组成。我们提供了与L相关的新Lax-Oleinik型算子族的收敛速度的上界估计，该算子族是由Wang和Yan （2012 Commun）的作者引入的。数学。物理学报，309 663-91)。此外，我们构造了一个由一个双曲周期轨道组成的时间无关正定拉格朗日系统的Aubry集，且当t→+∞时，Lax-Oleinik半群的收敛速率不能优于O（1/t）的例子。
Assume that the Aubry set of the time-periodic positive definite Lagrangian L consists of one hyperbolic 1-periodic orbit. We provide an upper bound estimate of the rate of convergence of the family of new Lax–Oleinik type operators associated with L introduced by the authors in Wang and Yan (2012 Commun. Math. Phys. 309 663–91). In addition, we construct an example where the Aubry set of a time-independent positive definite Lagrangian system consists of one hyperbolic periodic orbit and the rate of convergence of the Lax–Oleinik semigroup cannot be better than O(1/t) as t → +∞.