Invariants of twist-wise flow equivalence (Q1576785)

Let \(A\) be an \(n\times n\) nonnegative integer matrix. Then \(PS (A)= \det(I-A)\), and \(BF(A)={\mathbb{Z}^n \over(I-A) \mathbb{Z}^n}\) are called the Parry-Sullivan number and the Bowen-Frames group, respectively. It is known that for nontrivial irreducible incidence matrices flow equivalence of matrices is completely determined by two computable invariants, that is by \(PS(A)\) and \(BF(A)\). Here the author deals with the twist-wise flow equivalence which is a natural generalization of the above mentioned one and takes account of twisting in the local stable manifold of the orbits of a flow. Two new invariants in this category are presented.