Dynamics of a two parameter family of plane birational maps: Maximal entropy
Dynamics of a two parameter family of plane birational maps: Maximal entropy
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平面双有理映射的二参数族动力学：最大熵
DOI：
10.1007/bf02922060
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
J. Diller
中科院分区：
文献类型：
--
作者：
E. Bedford;J. Diller
本文将组合方法与复形方法相结合，研究了一类真实的双参数平面双有理映射族的动力学性质。具体地说，我们考虑的行动的映射的皮卡德群的一个适当的紧化的复平面上的同调群的前向不变的真实的子集的这种紧化，并在马尔可夫划分的真实的平面的临界集。对于所考虑的参数范围，这三个动作是等效的。这使我们能够在真实的非游荡集上构造一个最大熵的测度，并且它使我们能够证明所有游荡点都以一种定义明确的方式被吸引到无穷大。
We mix combinatorial with complex methods to study the dynamics of a real two parameter family of plane birational maps. Specifically, we consider the action of the maps on the Picard group of an appropriate compactification of the complex plane, on the homology groups of a forward invariant real subset of this compactification, and on a Markov partition of the real plane determined by the critical set. For the range of parameters considered, the three actions are equivalent. This allows us to construct a measure of maximal entropy on the real nonwandering set, and it allows us to show that all wandering points are attracted to infinity in a well-defined fashion.