Arnold Mathematical Journal
SCOPUS (2015-2024)
2199-6806
2199-6792
Thụy Sĩ
Cơ quản chủ quản: Springer International Publishing AG
Lĩnh vực:
Mathematics (miscellaneous)
Phân tích ảnh hưởng
Các bài báo tiêu biểu
On the Geometry of the Set of Symmetric Matrices with Repeated Eigenvalues
Tập 4 Số 3-4 - Trang 423-443 - 2018
Abstract We investigate some geometric properties of the real algebraic variety
$$\Delta $$ Δ of symmetric matrices with repeated eigenvalues. We explicitly
compute the volume of its intersection with the sphere and prove a
Eckart–Young–Mirsky-type theorem for the distance function from a generic matrix
to points in $$\Delta $$ Δ . We exhibit connections of our study to real
algebraic geometry (co...
Constructive Geometrization of Thurston Maps and Decidability of Thurston Equivalence
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Solvability of Equations by Quadratures and Newton’s Theorem
Tập 4 - Trang 193-211 - 2018
Picard–Vessiot theorem (1910) provides a necessary and sufficient condition for
solvability of linear differential equations of order n by quadratures in terms
of its Galois group. It is based on the differential Galois theory and is rather
involved. Liouville in 1839 found an elementary criterium for such solvability
for $$n=2$$ . Ritt simplified Liouville’s theorem (1948). In 1973 Rosenlicht
pro...