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A section in the 2-jet space of Morse functions is not always homotopic to a holonomic section. We give a necessary condition for being the case and we discuss the sufficiency.
There are examples of complete spacelike surfaces in the Lorentzian product ℍ2 × ℝ1 with constant Gaussian curvature K ≤ −1. In this paper, we show that there exists no complete spacelike surface in ℍ2 × ℝ1 with constant Gaussian curvature K > −1.
In this paper, first, we determine the quotient groups of the Hecke groups H(λ
), where q ≥ 7 is prime, by their principal congruence subgroups H
) oflevel p, where p is also prime. We deal with the case of q = 7 separately, because of its close relation with the Hurwitz groups. Then,...
A subgroup H of a group G is said to be M-supplemented in G if there exists a subgroup B of G such that G = HB and T B < G for every maximal sub-group T of H. Moreover, a subgroup H is called c-supplemented in G if there exists a subgroup K such that G = HK and H ∩ K ≤ H
We study the dynamics near an equilibrium point p
0 of a Z
2(ℝ)-reversible vector field in ℝ2n
with reversing symmetry R satisfying R
2 = I and dimFix(R) = n. We deal with one-parameter families of such systems X
λ such that X
0 presents at p
0 a degenerate resonance of type 0: p: q. We are...
The aim of this paper is twofold: Firstly, we generalize well-known formulas for ramification and different exponents in cyclic extensions of function fields over a field K (due to H. Hasse) to extensions E = F(y), where y satisfies an equation of the form f(y) = u · g(y) with polynomials f(y),...
We provide an affirmative answer to the C
-Closing Lemma, r ≥ 2, for a large class of flows defined on every closed surface.
We consider a one-sided transitive subshift of finite type σ: Σ → Σ and a Hölder observable A. In the ergodic optimization model, one is interested in properties of A-minimizing probability measures. If Ā denotes the minimizing ergodic value of A, a sub-action u for A is by definition a...
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