复多项式的拓扑熵是在Thurston的倡导下发展起来的一个新的研究领域。Thurston提出用一个新的统计量“核拓扑熵”来描述多项式的动力系统，并希望能够通过它给高次多项式参数空间一个量化的描述。. 本项目计划按照Thurston的想法系统的研究高次多项式的核拓扑熵。我们希望首先得到临界有限多项式的核拓扑熵算法；然后以此为基础来研究核拓扑熵是如何随参数变化的；最后把核拓扑熵的变化反映到参数空间，从而得到关于高次多项式参数空间connected locus的一个量化描述和一些组合结构、拓扑结构上的刻画。

The topic of the core entropy of complex polynomials is a new research field started by Thurston. He proposes a new.quantity, called "core entropy", to describe the dynamics of polynomials , and hopes it avalible to be applied to study the parameter spaces of polynomials of high degrees. . . This project will investigate the core entropy of complex polynomials by Thurston's plan. Firstly, we expect to obtain an algorithm used to compute the core entropy for polynomials. Based on this algorithm, we then begin to study the variation of the core entropy. Finally, by the variation of core entropies, we hope to give a quantitive description of the parameter spaces of polynomials with high degrees, including some combinatorial and topological structures of the spaces.