复杂动力系统的退化
Degenerations of Complex Dynamical Systems
摘要：
证明了黎曼球面上任意退化有理映射序列的最大测度的弱极限必定是可数原子和。对于一个单参数有理映射族f_t，我们改进了这个结果，证明了当该族退化时，极大熵测度在黎曼球面上有唯一的极限。族f_t可以看作是在t中形式Puienix级数的完备域上的Berkovich投影线上的一个有理函数，黎曼球面上的极限测度是与Berkovich线上的平衡测度相联系的“剩余测度”.为了证明，我们引入了一种新的技术，量化措施的Berkovich投影线，并证明了解决方案的唯一性的量化版本的拉回公式的平衡测度有。
英文摘要：
We show that the weak limit of the maximal measures for any degenerating sequence of rational maps on the Riemann sphere must be a countable sum of atoms. For a 1-parameter family f_t of rational maps, we refine this result by showing that the measures of maximal entropy have a unique limit on the Riemann sphere as the family degenerates. The family f_t may be viewed as a single rational function on the Berkovich projective line over the completion of the field of formal Puiseux series in t, and the limiting measure on the Riemann sphere is the "residual measure" associated to the equilibrium measure on the Berkovich line. For the proof, we introduce a new technique for quantizing measures on the Berkovich projective line and demonstrate the uniqueness of solutions to a quantized version of the pullback formula for the equilibrium measure there.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
