Related papers: Fatou Components with Punctured Limit Sets

Motivated by the question whether a round disk can be realized as the rotation set of a torus diffeomorphism, we study the roundness of rotation sets of a parametric family of torus diffeomorphisms $F_\rho$, where the parameter $\rho$…

We investigate the discontinuity of codings for the Julia set of a quadratic map. To each parameter ray, we associate a natural coding for Julia sets on the ray. Given a hyperbolic component $H$ of the Mandelbrot set, we consider the…

We look at the maximal entropy (MME) measure of the boundaries of connected components of the Fatou set of a rational map of degree greater than or equal to 2. We show that if there are infinitely many Fatou components, and if either the…

We define the stack of $G$-local systems with restricted variation on the formal puntured disc and study its properties. We embed sheaves of categories over this stack into the category of factorization module categories over…

It is proved that the fixed point submonoid and the periodic point submonoid of a trace monoid endomorphism are always finitely generated. Considering the Foata normal form metric on trace monoids and uniformly continuous endomorphisms, a…

Let $\boldsymbol{\Sigma}:=(\Sigma,\mathbb{M},\mathbb{P})$ be a surface with marked points $\mathbb{M}\subset\partial\Sigma\neq\varnothing$ on the boundary, and punctures $\mathbb{P}\subset\Sigma\setminus\partial\Sigma$, and $T$ an arbitrary…

A classical theorem of Fatou asserts that the Radon-Nikodym derivative of any finite positive Borel measure, $\mu$, with respect to Lebesgue measure on the complex unit circle, is recovered as the non-tangential limits of its Poisson…

We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\cn{n}$ fixing the orbits of a regular vector field. We reduce the formal classification problem to solve a…

We give an estimate of the discontinuity of the large Julia set for a perturbation of a class of maps tangent to the identity, by means of a two-dimensional Lavaurs Theorem. We adapt to our situation a strategy due to Bedford, Smillie and…

We show that fixed dimensional klt weak Fano pairs with alpha-invariants and volumes bounded away from $0$ and the coefficients of the boundaries belonging to a fixed DCC set $S$ form a bounded family. Moreover, such pairs admit a strong…

We introduce a novel approach linking fractal geometry to partially hyperbolic dynamics, revealing several new phenomena related to regularity jumps and rigidity. One key result demonstrates a sharp phase transition for partially hyperbolic…

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and…

There are several classes of transcendental entire functions for which the Julia set consists of an uncountable union of disjoint curves each of which joins a finite endpoint to infinity. Many authors have studied the topological properties…

In this paper we study holomorphic properties of infinite dimensional spin factors. Among the infinite dimensional Banach spaces with homogeneous open unit balls, we show that the spin factors are natural outlier spaces in which to ask the…

Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…

The symmetric group S_n acts as a reflection group on CP^{n-2} (for $n\geq 3$) . Associated with each of the $\binom{n}{2}$ transpositions in S_n is an involution on CP^{n-2} that pointwise fixes a hyperplane--the mirrors of the action. For…

Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact sets, where each set is a…

We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials and indicate potential for extensions. As our main tool, we show that for a large class of Newton maps that includes all hyperbolic…

We describe the rings of invariants for the finite orthogonal groups of plus type in odd characteristic acting on the defining representations. We also describe the invariants of the corresponding Sylow subgroups in the defining…

We consider polynomial maps $f:\C\to\C$ of degree $d\ge 2$, or more generally polynomial maps from a finite union of copies of $\C$ to itself which have degree two or more on each copy. In any space $\p^{S}$ of suitably normalized maps of…