Arnold Mathematical Journal
Công bố khoa học tiêu biểu
* Dữ liệu chỉ mang tính chất tham khảo
Sắp xếp:
Solvability of Equations by Quadratures and Newton’s Theorem
Arnold Mathematical Journal - 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...
Homology of Spaces of Non-Resultant Homogeneous Polynomial Systems in $${\mathbb R}^2$$ and $${\mathbb C}^2$$
Arnold Mathematical Journal - Tập 1 - Trang 233-242 - 2015
The resultant variety in the space of systems of homogeneous polynomials of some
given degrees consists of such systems having non-trivial solutions. We
calculate the integer cohomology groups of all spaces of non-resultant systems
of polynomials $${\mathbb R}^2 \rightarrow {\mathbb R}$$ , and also the rational
cohomology rings of spaces of non-resultant systems and non-m-discriminant
polynomials ...
Invariant Spanning Trees for Quadratic Rational Maps
Arnold Mathematical Journal - Tập 5 - Trang 435-481 - 2019
We study Thurston equivalence classes of quadratic post-critically finite
branched coverings. For these maps, we introduce and study invariant spanning
trees. We give a computational procedure for searching for invariant spanning
trees. This procedure uses bisets over the fundamental group of a punctured
sphere. We also introduce a new combinatorial invariant of Thurston classes—the
ivy graph.
A Formula for the HOMFLY Polynomial of rational links
Arnold Mathematical Journal - Tập 1 - Trang 345-359 - 2015
We give an explicit formula for the HOMFLY polynomial of a rational link (in
particular, knot) in terms of a special continued fraction for the rational
number that defines the given link [after this work was accomplished, the
authors learned about a paper by Nakabo (J. Knot Theory Ramif 11(4):565–574,
2002) where a similar result was proved. However, Nakabo’s formula is different
from ours, and h...
Centralizers in Mapping Class Groups and Decidability of Thurston Equivalence
Arnold Mathematical Journal - Tập 6 - Trang 271-290 - 2020
We find a constructive bound for the word length of a generating set for the
centralizer of an element of the Mapping Class Group. As a consequence, we show
that it is algorithmically decidable whether two postcritically finite branched
coverings of the sphere are Thurston equivalent.
Localization Properties of Chern Insulators
Arnold Mathematical Journal - Tập 5 - Trang 15-21 - 2019
We study the localization properties of the equal-time electron Green’s function
in a Chern insulator in an arbitrary dimension and with an arbitrary number of
bands. We prove that the Green’s function cannot decay super-exponentially if
the Hamiltonian is finite-range and the quantum Hall response is nonzero. For a
general band Hamiltonian (possibly infinite-range), we prove that the Green’s
func...
A Galois–Dynamics Correspondence for Unicritical Polynomials
Arnold Mathematical Journal - Tập 7 - Trang 467-481 - 2021
In an analogy with the Galois homothety property for torsion points of abelian
varieties that was used in the proof of the Mordell–Lang conjecture, we describe
a correspondence between the action of a Galois group and the dynamical action
of a rational map. For nonlinear polynomials with rational coefficients, the
irreducibility of the associated dynatomic polynomial serves as a convenient
criteri...
More About Areas and Centers of Poncelet Polygons
Arnold Mathematical Journal - Tập 7 - Trang 91-106 - 2020
We study the locus of the Circumcenter of Mass of Poncelet polygons, and the
limit of the Center of Mass (when we consider the polygon as a “homogeneous
lamina”) for degenerate Poncelet polygons. We also provide a proof for one of
Dan Reznik invariants for billiard trajectories. Plus, we take a look at how the
scene looks like when we shift to spherical geometry.
Space of Smooth 1-Knots in a 4-Manifold: Is Its Algebraic Topology Sensitive to Smooth Structures?
Arnold Mathematical Journal - Tập 1 Số 1 - Trang 83-89 - 2015
Generalized Plumbings and Murasugi Sums
Arnold Mathematical Journal - Tập 2 - Trang 69-119 - 2015
We propose a generalization of the classical notions of plumbing and Murasugi
summing operations to smooth manifolds of arbitrary dimensions, so that in this
general context Gabai’s credo “the Murasugi sum is a natural geometric
operation” holds. In particular, we prove that the sum of the pages of two open
books is again a page of an open book and that there is an associated summing
operation of ...
Tổng số: 155
- 1
- 2
- 3
- 4
- 5
- 6
- 10