链双曲同宿类上周期偏差现象的研究

The Research of the Periodic Deviation Phenomenon on the Chain Hyperbolic Homoclinic Class

具有链双曲性质的同宿类,它是部分双曲系统中最典型也是人们研究最多的一类。本文研究的是此类集合上具有偏差性质的周期轨道,我们将利用广义测度熵这个新概念来刻画偏差周期轨的指数增长率。

The homoclinic class with chain hyperbolicity is a typical kind of partially hyperbolic system. It has gained more and more attention from researchers. This paper concerns the periodic measures with deviation in such homoclinic class. By the generalized metric entropy, we give the upper bound of the exponential growth rate of the deviated periodic measures.