非线性代数动力系统的拟合理想
Fitting ideals for finitely presented algebraic dynamical systems
摘要：
本文考虑了Kittern和Schmidt提出的一类代数动力系统。在弱有限性条件--降链条件下，对偶模具有有限表示.使用方法从交换代数，我们展示了如何系统的动力学性质可以推导出从拟合理想的一个有限的自由分解的一个有限提出的模块。熵和膨胀性仅取决于第一拟合理想（和某些多重性数据），这给出了一个简单的计算：特别是，没有syzygy模块需要计算。对于“广场”介绍（其中发电机的数量等于关系的数量）的所有动态是可见的第一拟合理想和某些多重性数据，我们展示了如何的动力学性质和周期点的行为可以推导出关系矩阵的行列式。
英文摘要：
We consider a class of algebraic dynamical systems introduced by Kitchens and Schmidt. Under a weak finiteness condition -- the Descending Chain Condition -- the dual modules have finite presentations. Using methods from commutative algebra we show how the dynamical properties of the system may be deduced from the Fitting ideals of a finite free resolution of the finitely presented module. The entropy and expansiveness are shown to depend only on the first Fitting ideal (and certain multiplicity data) which gives an easy computation: in particular, no syzygy modules need to be computed. For `square' presentations (in which the number of generators is equal to the number of relations) all the dynamics is visible in the first Fitting ideal and certain multiplicity data, and we show how the dynamical properties and periodic point behaviour may be deduced from the determinant of the matrix of relations.
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