When the saddle-center bifurcation occurs in an analytic family of area-preserving maps, rst a parabolic xed point appears at the origin and then this point bi-furcates, creating an elliptic xed point and a hyperbolic one. Separatrices of the hyperbolic xed point form a small loop around the elliptic point. In general the sep-aratrices intersect transversely and the splitting is exponentially s...

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...

In her thesis [RB], Ranee Brylinski (then Gupta) studied the orbit structure of the projective variety of abelian subalgebras of a …xed dimension, k, in a simple Lie algebra, g, over C under its adjoint group, G. Fix a Borel subalgebra, b, of g and let B be the closed subgroup of G corresponding to b. Then the Borel …xed point theorem implies that the closed G-orbits are precisely the orbits of...

in this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.

in the present paper, measure differential equations involving the distributional henstock-kurzweil integral are investigated. theorems on the existence and structure of the set of solutions are established by using schauder$^prime s$ fixed point theorem and vidossich theorem. two examples of the main results paper are presented. the new results are generalizations of some previous results in t...

Verifying a 64-bit multiplier has a computational complexity that puts it beyond the grasp of current nite-state algorithms, including those based upon homomorphic reduction, the induction principle, and bdd xed-point algorithms. Theorem proving, while not bound by the same computational constraints, may not be feasible for routinely coping with the complex, low-level details of a real multipli...

We consider the action of the symmetric group S n on the Schubert poly-nomials of xed degree. This action induces a well known family of representations of S n. We point on Kazhdan-Lusztig structures which appear in these representations. First, a combinatorial rule for restricting these representations to Young subgroups is obtained. This rule is an exact analogue of Barbasch-Vogan's rule for ...

| In this paper we describe a new technique for proving that a particular system is chaotic in topological sense, i.e. that it has positive topological entropy. This technique combines existence results based on the xed point index theory and computer-assisted computations, necessary to verify assumptions of the existence theorem. First we present an existence theorem for periodic points of map...

We present a new embedding theorem for time series, in the spirit of Takens's theorem, but requiring multivariate signals. Our result is part of a growing body of work that extends the domain of geometric time series analysis to some genuinely stochastic systems|including such natural examples as xj+1 = (xj) + j where is some xed map and the j are i.i.d. random displacements.