Related papers: The Sullivan dictionary and Bowen-Series maps

This is an expository plus research paper which mainly exposes preliminary connection and contrast between classical complex dynamics and semigroup dynamics of holomorphic functions. Classically, we expose some existing results of rational…

We propose a generalization of the concept of a Ribbon graph suitable to provide combinatorial models for marked surfaces equipped with a G-structure. Our main insight is that the necessary combinatorics is neatly captured in the concept of…

It was proposed the Lie group such that symplectic structure of orbits of co-adjoint representation of the group is revealed symplectic structure of a rigid body dynamics in quaternion variables. It is shown that Poisson brackets of…

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical…

Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…

It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…

We introduce the notion of a rational dynamical system extending the classical notion of a topological dynamical system and we prove (multiple) recurrence results for such systems via a partition theorem for the rational numbers proved by…

Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin…

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…

Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description…

We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several important subspaces; a discussion…

Recently, a Lagrangian description of superfluids attracted some interest from the fluid/gravity-correspondence viewpoint. In this respect, the work of Dubovksy et al. has proposed a new field theoretical description of fluids, which has…

We prove that the dynamical Teichm\"uller space of a rational map immerses into the space of rational maps of the same degree, answering a question of McMullen and Sullivan. This is achieved through a new description of the tangent and…

For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical…

A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…

We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann…

We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin's theory and Quillen's + construction are developed. In the special case of…

We describe a variant of the popular game "Pictionary" based on terms used in elementary and high school physics. We believe that drawing of physical terms helps students develop a deeper understanding of physical concepts behind them, as…

We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed.…

This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…