Fredholm determinant for piecewise linear transformations
Fredholm determinant for piecewise linear transformations
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分段线性变换的 Fredholm 行列式
DOI：
10.18910/10418
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发表时间：
1990
影响因子：
0.4
通讯作者：
M. Mori
中科院分区：
文献类型：
--
作者：
M. Mori
我们称这个数为下李雅普诺夫数。我们将研究Spec^），P \BV的谱> P对有界变差函数的子空间BV的限制。P的生成函数由划分的分界点的轨道确定，并且轨道由更新方程（§ 3）定义的有限维矩阵Φ（z）表征。因此，我们可以证明，D（z）=det（I- Φ（λ）），我们称之为Fredholm行列式，在以下意义上是I-Φ P= Φ（λ）-Φ zP的行列式：定理A.设λ G C，并假设e~.则λ属于Sρec（F）当且仅当z-1 ~是D（z）的零点：
We call the number ξ the lower Lyapunov number. We will study Spec^) , the spectrum of P \BV> the restriction of P to the subspace BV of functions with bounded variation. The generating function of P is determined by the orbits of the division points of the partition, and the orbits are characterized by a finite dimensional matrix Φ(z) which is defined by a renewal equation (§ 3). Hence, we can show that D(z)=det(I— Φ(#))> which we call a Fredholm determinant, is the determinant of /— #P=ΣίΓ-o zP in the following sense: Theorem A. Let λ G C and assume that \\\>e~. Then λ belongs to Sρec(F) if and only if z—\~ is a zero of D(z):