In this article, we prove that for all pairs of primitive Pisot or uniform substitutions with the same dominating eigenvalue, there exists a finite set of block maps such that every block map between the corresponding subshifts is an element of this set, up to a shift. This result is proved using a common generalization of block maps and substitutions, which we call dill maps.

In this paper we propose a quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomialmapwhere theNewtonmethod is used to solve an equivalent system of nonlinear equations. The semi-symmetric tensor is introduced to reveal the relation between homogeneous polynomial map and its associated semi-symmetric tensor. Based on this relation a globally ...

In this paper, we prove that for every Finsler n-sphere (S, F ) for n ≥ 3 with reversibility λ and flag curvature K satisfying ( λ λ+1 )2 < K ≤ 1, either there exist infinitely many prime closed geodesics or there exists one elliptic closed geodesic whose linearized Poincaré map has at least one eigenvalue which is of the form exp(πiμ) with an irrational μ. Furthermore, there always exist three...

Based on the geometric theories of vector space, a Cross-Identity theorem is proved for the relationship between the power kernels and power images of linear map Α Ι − λ on its cyclic subspace. By this result, a new approach of proof is found for the fact that a square matrix with only one eigenvalue and one-dimensional eigenspace is similar to a Jordan block matrix.

A Hurwitz correspondence is a multi-valued self-map of the moduli space of genus zero curves with n marked points, M0,n. Considering two n-marked curves (C, a1, ..., an) and (D, b1, ..., bn), given a map ρ from {1, ..., n} to itself and some ramification data, one obtains a Hurwitz correspondence on M0,n which sends a marked curve (D, b1, ..., bn) to any of the marked curves (C, a1, ..., an) fo...

Cosmological solutions of a toy homogeneous isotropic universe filled with a superfluid Bose condensate described by a complex scalar field (with relativistic barotropic fluid interpretation) are studied. The eigenvalues of the tangent map for the resulting Hamiltonian system are used to classify the phase space regions and to understand the typical toy-universe evolution. After a transient, in...

It is known that the second dominant eigenvalue of a matrix determines the convergence rate of the power method. Though ineffective for general eigenvalue computation, the power method has been of practical usage for computing the stationary distribution of a stochastic matrix. For a Markov chain with memory m, the transition “matrix" becomes an order-m tensor. Under suitable assumptions, the s...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

We consider the class of graph-directed constructions which are connected and have the property of finite ramification. By assuming the existence of a fixed point for a certain renormalization map, it is possible to construct a Laplace operator on fractals in this class via their Dirichlet forms. Our main aim is to consider the eigenvalues of the Laplace operator and provide a formula for the s...