频繁超循环整函数与缓慢增长
Frequently hypercyclic meromorphic curves with slow growth
AI总结：
研究通过Nevanlinna理论和Oka原理，构造了在射影空间中具有缓慢增长的频繁超循环整函数，并揭示了在增长约束下频繁超循环性质的二元对立。
摘要：
我们构造了在射影空间中表现出频繁超循环性质的整函数，这些函数在沿可数多个预设方向上进行平移时保持最优的缓慢增长速率。此外，我们通过证明在等价增长约束下，无法同时保持频繁超循环性质对于不可数多个方向，建立了基本的二元对立。这一结果与经典超循环现象形成鲜明对比，其中整个函数可以在某些不可数方向集上实现超循环而不牺牲增长速率。我们的方法基于Nevanlinna理论并受到Oka原理的指导，为理解射影空间中整函数的动力学性质与增长速率之间的关系提供了新的见解。
英文摘要：
We construct entire curves in projective spaces that exhibit frequent hypercyclicity under translations along countably many prescribed directions while maintaining optimal slow growth rates. Furthermore, we establish a fundamental dichotomy by proving the impossibility of such curves simultaneously preserving frequent hypercyclicity for uncountably many directions under equivalent growth constraints. This result reveals a striking contrast with classical hypercyclicity phenomena, where entire functions can achieve hypercyclicity over some uncountable direction set without growth rate compromise. Our methodology is rooted in Nevanlinna theory and guided by the Oka principle, offering new insights into the relationship between dynamical properties and growth rates of entire curves in projective spaces.
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