Hypercyclic abelian subgroups of GL(n, ℝ)

Geodesic bases for Lie algebras

“…Then φ(X) > 0 when x 1 > 0 and φ(X) < 0 when x 1 < 0 (or vice versa), so by continuity, φ(X) = 0 when x 1 = 0, so φ is a product of x 1 by a linear form, which must again be a multiple of x 1 , as all the zeros of φ lie in the hyperplane x 1 = 0. So φ = cx 2 1 , a contradiction. Therefore it is sufficient to find a symmetric positive definite G such that φ is indefinite.…”

“…It follows that for a basis of geodesic elements for g to exist it suffices that such a basis exists for n (and the same is true for orthonormal bases). A nonzero vector X ∈ n is geodesic if and only if (2) A j X, X = 0, for all j = 1, . .…”

线性算子动力系统的研究进展

“…在线性算子动力系统中, 存在超循环的算子族, 使得该算子族不存在公共的超 循环向量, 可参见文献 [69]. Ayadi 等学者在文献 [70] [72,73] 的工作以及 Desch 等学者在文献 [74] 研究的基础上, Liang 和 Zhou [75] 讨论了复扇形区域上平移算子半群的亚超循环性质, 并给出了下面结论: [77] [78]…”

On multi-hypercyclic abelian semigroups of matrices on $\mathbb{R}^{n}$

“…3. Abelian sub-semigroup of K * η,r,r (R) with a locally dense orbit The aim of this section is to give results for abelian sub-semigroups of K * η,r,s (R) analogous to those for abelian groups in ( [3], Sections 3, 4 and 7).…”