Related papers: Rotation number for a homogeneous vector field in …

We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…

We investigate the transfer of regularity between commutative, noetherian, local rings through a class of local homomorphisms which we call basically regular. We give numerical characterizations of these maps, investigate their behavior…

Let $M$ be a smooth ($C^{\infty}$) manifold, $F_1,...,F_n$ be vector fields on $M$ generating the corresponding flows $\Phi_1,...,\Phi_n$, and $\alpha_1,...,\alpha_{n}:M\to \mathbb{R}$ smooth functions. Define the following map $f:M\to M$…

We consider an orientation preserving homeomorphism $h$ of $S^2$ which admits a repellor denoted $\infty$ and an attractor $-\infty$, which is not a North-South map, such that the basins of $\infty$ and $-\infty$ intersect. We study various…

In this paper we denote a type of affine homogeneous real hypersurface of $\mathbb{C}^3$ and present a classification of homogeneous surfaces of the type (1/2,0). The result was obtained by reducing the classification problem mentioned…

Motion of test particles along rotating curved trajectories is considered. The problem is studied both in the laboratory and the rotating frames of reference. It is assumed that the system rotates with the constant angular velocity $\omega…

In this work we define the trajectory coset of an affine map and use it to study the similarity classes of affine maps. We use the trajectory coset, a tool which allows us to gain a deeper understanding of the interplay between geometry…

In this paper, we classify the rotational surfaces with constant skew curvature in $3$-space forms. We also give a variational characterization of the profile curves of these surfaces as critical points of a curvature energy involving the…

The Poincare-Hopf theorem tells us that given a smooth, structurally stable vector field on a surface of genus g, the number of saddles is 2-2g less than the number of sinks and sources. We generalize this result by introducing a more…

This paper devoted to proof the existence of stable quasi-periodic motions of the magnetic dipole that is under the action of the external magnetic field and homogeneous field of gravity. For proof this we used the group-theoretic methods…

We use finite connectivity equilibrium replica theory to solve models of finitely connected unit-length vectorial spins, with random pair-interactions which are of the orthogonal matrix type. Since the spins are continuous and the…

We give a geometrical demonstration to the existence of holomorphic first integrals for certain kind of vector fields in $\mathbb{C}^2$ and $\mathbb{C}^3$.

We study equations of a non-gauge vector field in a spherically symmetric static metric. The constant vector field with a scale arrangement of components: the time component about the Planck mass m_{Pl} and the radial component about M…

We develop and analyze a random field model for the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities provided by RANS simulations that is accessible to both a rigorous analytical validation…

We study the connectedness locus $\mathcal{N}$ for the family of iterated function systems of pairs of homogeneous affine-linear maps in the plane. We prove this set is regular closed (i.e., it is the closure of its interior) away from the…

A study of proper conformal vector field in non conformally flat cylindrically symmetric static space-times is given by using direct integration technique. Using the above mentioned technique we have shown that a very special class of the…

Let R be a commutative ring with 1. For every homogeneous polynomial f(X_0,X_1,X_2) in R[X_0,X_1,X_2] of degree d <= 25, we find a explicit linear Pfaffian R-representation of f. We describe an empirical method that leads us to find such…

We develop a "metrically selfdual" variational calculus for $c$-monotone vector fields between general manifolds $X$ and $Y$, where $c$ is a coupling on $X\times Y$. Remarkably, many of the key properties of classical monotone operators…

Direct numerical simulations are performed to study turbulent Rayleigh-B\'{e}nard convection in a vertical cylindrical cavity with uniform axial magnetic field. Flows at high Hartmann and Rayleigh numbers are considered. The calculations…

Dynamical systems on an infinite translation surface with the lattice property are studied. The geodesic flow on this surface is found to be recurrent in all but countably many rational directions. Hyperbolic elements of the affine…