Let C v be a complete, algebraically closed non-archimedean field, and let f ∈ ( z ) rational function of degree d ≥ 2 . If satisfies bounded contraction condition on its Julia set, we prove that small perturbations have dynamics conjugate to those their sets.

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential for...

We explore the distinction between convergence and absolute convergence of series in both Archimedean and non-Archimedean ordered fields and find that the relationship between them is closely connected to sequential (Cauchy) completeness.

The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordina...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

Copulas [18] link univariate marginal distribution functions into a joint distribution function of the corresponding random vector. In this paper we will deal with bivariate copulas only. Recall that a function C : [0, 1] → [0, 1] is a (bivariate) copula whenever it is grounded, C(x, y) = 0 whenever 0 ∈ {x, y}, it has neutral element 1, C(x, y) = x∧y, whenever 1 ∈ {x, y} and it is 2-increasing,...

If ρ is a selfdual representation of a group G on a vector space V over C, we will say that ρ is orthogonal, resp. symplectic, if G leaves a nondegenerate symmetric, resp. alternating, bilinear form B : V ×V → C invariant. If ρ is irreducible, exactly one of these possibilities will occur, and we may define a sign c(ρ) ∈ {±1}, taken to be +1, resp. −1, in the orthogonal, resp. symplectic, case....

In the first part of the paper we generalize a descent technique due to HarishChandra to the case of a reductive group acting on a smooth affine variety both defined over arbitrary local field F of characteristic zero. Our main tool is Luna slice theorem. In the second part of the paper we apply this technique to symmetric pairs. In particular we prove that the pair (GLn(C), GLn(R)) is a Gelfan...

In the first part of the paper we generalize a descent technique due to HarishChandra to the case of a reductive group acting on a smooth affine variety both defined over arbitrary local field F of characteristic zero. Our main tool is Luna slice theorem. In the second part of the paper we apply this technique to symmetric pairs. In particular we prove that the pair (GLn(C), GLn(R)) is a Gelfan...

In the first part of the paper we generalize a descent technique due to HarishChandra to the case of a reductive group acting on a smooth affine variety both defined over arbitrary local field F of characteristic zero. Our main tool in that is Luna slice theorem. In the second part of the paper we apply this technique to symmetric pairs. In particular we prove that the pair (GLn(C), GLn(R)) is ...