Maximizing measures for partially hyperbolic systems with compact center leaves
Maximizing measures for partially hyperbolic systems with compact center leaves
复制标题
最大化具有紧凑中心叶片的部分双曲系统的措施
DOI：
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发表时间：
2010
影响因子：
0.9
通讯作者：
R. Ures
中科院分区：
文献类型：
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作者：
F. R. Hertz;M. R. Hertz;A. Tahzibi;R. Ures
对于具有紧中心叶的三维流形的可达部分双曲微分同胚，我们得到了如下二分法：要么存在唯一的具有Bernoulli性质且中心Lyapunov指数为0的极大熵测度，要么存在有限个中心Lyapunov指数非零的极大熵测度(至少一个具有负指数，一个具有正指数)，它们都是Bernoulli系统的有限推广.在二分法的第一种情况下，我们得到了该系统与双曲型系统的旋转扩张拓扑共轭。这意味着，在我们的结果的假设中，二分法的第二种情况适用于一组开放的稠密的微分同胚集。作为结果，我们得到了一个拓扑混合微分同胚的开集，它具有多于一个的最大熵测度。
Abstract We obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-dimensional manifolds having compact center leaves: either there is a unique entropy-maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0, or there are a finite number of entropy-maximizing measures, all of them with non-zero center Lyapunov exponents (at least one with a negative exponent and one with a positive exponent), that are finite extensions of a Bernoulli system. In the first case of the dichotomy, we obtain that the system is topologically conjugated to a rotation extension of a hyperbolic system. This implies that the second case of the dichotomy holds for an open and dense set of diffeomorphisms in the hypothesis of our result. As a consequence, we obtain an open set of topologically mixing diffeomorphisms having more than one entropy-maximizing measure.