Related papers: A two-dimensional polynomial mapping with a wander…

We are concerned with polynomial involutions in characteristic two. In this note, we look for involutions among triangular automorphisms of the four-dimensional polynomial ring in characteristic two and obtain three types of such…

We build saddle measures (in a weak sense) for holomorphic endomorphisms of CP^2.

In this note, we are interested in the Jacobian Conjecture. Following the results of L.M.~Dru$\dot{\rm z}$kowski, we consider some vector fields depending on a certain \'etale polynomial map. From results of semialgebraic geometry with the…

Chebyshev maps in the complex plane are typical chaotic maps. Veselov generalized these map. We consider a class of those maps and view them as holomorphic endomorphisms on the 3-dimensional complex projective space and make use of the…

We prove the multisummability of the infinitesimal generator of unfoldings of finite codimension tangent to the identity 1-dimensional local complex analytic diffeomorphisms. We also prove the multisummability of Fatou coordinates and…

We study the internal dynamics of multiply connected wandering domains of meromorphic functions. We do so by considering the sequence of injectivity radii along the orbit of a base point, together with the hyperbolic distortions along the…

In the present paper we investigate the existence of directional derivatives for strongly cone-paraconvex mappings. Our result is a counterpart of the theorem of Valadier concerning directional differentiability of cone convex mappings.

We construct one and two parameter deformations of the two dimensional Chebyshev polynomials with simple recurrence coefficients, following the algorithm in [3]. Using inverse scattering techniques, we compute the corresponding…

In this paper, we consider a one-parameter family of degree $d\ge 2$ rational maps with an automorphism group containing the cyclic group of order $d$. We construct a polynomial whose roots correspond to parameter values for which the…

Let $F=(F_1,F_2):C^2 ---> C^2 be a polynomial automorphism. It is well know that deg F_1 | deg F_2 or deg F_2 | deg F_1. On the other hand, if (d_1,d_2) \in (N\{0})^2 is such that d_1 | d_2 or d_2 | d_1, then one can construct a polynomial…

In this paper, we discuss duality about components of invariant variety of periodic points(IVPP) and fundamental domain of recurrence equation, and present an algorithm for the derivation of all components of IVPPs of any rational maps. It…

We study the polynomial entropy of the wandering part of any invertible dynamical system on a compact metric space. As an application we compute the polynomial entropy of Brouwer homeomorphisms (fixed point free orientation preserving…

A step 2 branching decomposition of spaces of homogeneous Hermitian monogenic polynomials in C^n is established with explicit embedding factors in terms of the generalized Jacobi polynomials, which allows for an inductive construction of an…

We study analytic deformations and unfoldings of holomorphic foliations in complex projective plane $\mathbb{C}P(2)$. Let $\{\mathcal{F}_t\}_{t \in \mathbb{D}_{\epsilon}}$ be topological trivial (in $\mathbb{C}^2$) analytic deformation of a…

In this paper we show that if $p$ is a polynomial which bifurcates then the product map $(z,w)\mapsto(p(z),q(w))$ can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets…

We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asymptotic expansion in the power-iterated log scale.

Let $f$ be a post-critically finite endomorphism (PCF map for short) on $\mathbb{P}^2$, let $J_1$ denote the Julia set and let $J_2$ denote the support of the measure of maximal entropy. In this paper we show that: 1. $J_1\setminus J_2$ is…

We prove two results about degree of polynomial mappings of $C^2$ to $C^2$.

We consider a partially hyperbolic C1-diffeomorphism f on a smooth compact manifold M with a uniformly compact f-invariant center foliation. We show that if the unstable bundle is one-dimensional and oriented, then the holonomy of the…

We observe that there exists an associative finite dimensional $\mathbb{C}$-algebra $A$ of finite global dimension, such that the bounded derived category $D^b(A)$ of finite dimensional $A$-modules admits an admissible subcategory…