for the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. when the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. in this paper we will consider the polynomial planar vector fields ...

For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...

The current work focuses on critical exponents of the two-dimensional ferromagnetic Ising model defined on the hyperbolic plane. The hyperbolic plane is a simply connected infinite surface in which the Gaussian curvature possesses a constant negative curvature at arbitrary points. This non-zero curvature changes the geometric symmetry of the embedded Ising lattice model, and thus possibly induc...

We study the dynamics of a holomorphic self-map f of complex projective space of degree d > 1 by utilizing the notion of a Fatou map, introduced originally by Ueda (1997) and independently by the author (2000). A Fatou map is intuitively like an analytic subvariety on which the dynamics of f are a normal family (such as a local stable manifold of a hyperbolic periodic point). We show that globa...

We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. by consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic length, we motivate a reformulation of the basic equation of conformal covariance. The scale factors gain a new, physical interpretation. We exhibit a fully ...

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

We describe an algorithm for distinguishing hyperbolic components in the parameter space of quadratic rational maps with a periodic critical point. We then illustrate computer images of the hyperbolic components of the parameter spaces V1 − V4, which were produced using our algorithm. We also resolve the singularities of the projective closure of V5 by blowups, giving an alternative proof that ...