Related papers: On Rational Maps with Two Critical Points

In this paper we study the dynamics of rational maps induced by endomorphisms of ordinary elliptic curves defined over finite fields.

We study subelliptic biharmonic maps, i.e. smooth maps from a compact strictly pseudoconvex CR manifold M into a Riemannian manifold N which are critical points of a certain bienergy functional. We show that a map is subelliptic biharmonic…

A rational map with good reduction in the field $\mathbb{Q}\_p$ of $p$-adic numbers defines a $1$-Lipschitz dynamical system on the projective line $\mathbb{P}^1(\mathbb{Q}\_p)$ over $\mathbb{Q}\_p$. The dynamical structure of such a system…

Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps…

It will be shown that the renormalization operator, acting on the space of smooth unimodal maps with critical exponent greater than 1, has periodic points of any combinatorial type.

We report on progress in the qualitative study of rational points on rationally connected varieties over number fields, also examining integral points, zero-cycles, and non-rationally connected varieties. One of the main objectives is to…

Many mathematicians encounter k-to-1 maps only in the study of covering maps. But, of course, k-to-1 maps do not have to be open. This paper touches on covering maps, and simple maps, but concentrates on ordinary k-to-1 functions (both…

A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the…

We outline an alternative approach to the geometric notion of a saddle point for real-valued functions of two variables. It is argued that this is more natural compared to the usual treatment of this topic in standard texts on Calculus.

Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the…

Observations on rational Chow groups and cycle class maps in equivariant contexts.

Semantic mapping is the incremental process of "mapping" relevant information of the world (i.e., spatial information, temporal events, agents and actions) to a formal description supported by a reasoning engine. Current research focuses on…

We survey some results on real rational surfaces focused on their topology and their birational geometry.

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

Let $K$ be a global function field of characteristic $p$ and degree $D$ over $\mathbb F_{p}(t)$. We consider dynamical systems over the projective line $\mathbb P^1(K)$ defined by rational maps with at most one prime of bad reduction. The…

In a given 2D space, we can have points with different levels of importance. One would prefer viewing those points from a closer/farther position per their level of importance. A point in 2D from where the user can view two given points per…

We discuss the bifurcation structure of homoclinic orbits in bimodal one dimensional maps. The universal structure of these bifurcations with singular bifurcation points and the web of bifurcation lines through the parameter space are…

We show that the set of conjugacy classes of cubic polynomials with a prefixed critical point, of preperiod $k\geq 1$, is an irreducible algebraic curve. We also establish an analogous result for quadratic rational maps. We then study a…

In this paper we study homeomorphisms of the circle with several critical points and bounded type rotation number. We prove complex a priori bounds for these maps. As an application, we get that bi-cubic circle maps with same bounded type…

In the last years the attention towards topological dynamical properties of highly discontinuous maps has increased significantly. In [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Math\'ematique, 360(G4),…