Energy and invariant measures for birational surface maps
Energy and invariant measures for birational surface maps
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双有理表面图的能量和不变测度
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
J. Diller
中科院分区：
文献类型：
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作者：
E. Bedford;J. Diller
给定一个紧复曲面的双有理自映射，找到一个将映射的动力学与其上同调作用联系起来的不变测度是有用的。在地图上一个非常弱的假设下，我们展示了如何构建这样的度量。构建的要点是理解两个正、闭合 (1, 1) 电流的楔积。在我们的例子中，我们能够做到这一点，因为每个电流的局部电势相对于另一个电流具有“有限能量”。我们的方法还足以表明所得测量是混合的，不影响曲线，并且具有非零李亚普诺夫指数。
Given a birational self-map of a compact complex surface, it is useful to find an invariant measure that relates the dynamics of the map to its action on cohomology. Under a very weak hypothesis on the map, we show how to construct such a measure. The main point in the construction is to make sense of the wedge product of two positive, closed (1, 1)-currents. We are able to do this in our case because local potentials for each current have ``finite energy' with respect to the other. Our methods also suffice to show that the resulting measure is mixing, does not charge curves, and has nonzero Lyapunov exponents.