Related papers: Classifying multiply connected wandering domains

This article explores the topology of Pseudo-B\"ottcher totally invariant connected components of the wandering set in dynamical systems generated by on-invertible inner (open surjective isolated) mappings of compact surfaces. We describe…

We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…

Traditionally, robots are regarded as universal motion generation machines. They are designed mainly by kinematics considerations while the desired dynamics is imposed by strong actuators and high-rate control loops. As an alternative, one…

Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…

In this paper we study two classes of meromorphic functions previously studied by Mayer, Kotus, and Urba\'nski. In particular we estimate a lower bound for the Julia set and the set of escaping points for non-autonomous additive and affine…

A meromorphic connection on the complex projective line induces formal connections at each singular point, and these formal connections constitute the local behavior at the singularities. In this primarily expository paper, we discuss the…

A wandering domain for a diffeomorphism is an open connected set whose iterates are pairwise disjoint. We endow A^n = T^n x R^n with its usual exact symplectic structure. An integrable diffeomorphism {\Phi}^h, i.e. the time-one map of a…

We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction,…

We construct the meromorphic functions invariant under the action of the sense-preserving wallpaper groups on the complex plane. We discuss possible generalisa-tions of this to the general wallpaper groups. This provides the answer to a…

The classical representation of Hamiltonian systems in terms of action-angle variables are defined for simply connected domains such as an interior of a homoclinic orbit. On this basis methods of (local) perturbations leading, in…

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…

We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…

We revisit the description of ferromagnetic domain wall dynamics through an extended one-dimensional model by allowing flexural distortions of the wall during its motion. This is taken into account by allowing the domain wall center and…

The classification of Fatou components for rational functions was concluded with Sullivan's proof of the No Wandering Domains Theorem in 1985. In 2016 it was shown, in joint work of the first and last author with Buff, Dujardin and Raissy,…

We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions. On the one hand, we prove that a bounded domain is a Fatou component of some meromorphic function if and only if it…

This paper continues our investigation of the dynamics of families of transcendental meromorphic functions with finitely many singular values all of which are finite. Here we look at a generalization of the family of polynomials…

The brain may be thought of as a many-body architecture with a spatio-temporal dynamics described by neuronal structures. The oscillatory nature of brain activity allows these structures (nodes) to be described as a set of coupled…

This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…

Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the…

In this paper, we investigate for the first time, the spatiotemporal dynamics of self-similar parabolic pulse evolution in multimode fibers (MMFs). We present numerical predictions of the existence of parabolic pulse in a graded and step…