Related papers: Orbit Portraits in non-Autonomous Iteration

In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…

The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…

We classify all topological phase portraits of the polynomial generalized Li\'enard system, determined by three arbitrary polynomials, at the origin and the infinity. This yields a complete characterization of monodromy at the origin and…

Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an…

We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…

We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the…

Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…

We construct new substantive examples of non-autonomous vector fields on 3-dimensional sphere having a simple dynamics but non-trivial topology. The construction is based on two ideas: the theory of diffeomorpisms with wild separatrix…

We prove exponential contraction of renormalization along hybrid classes of infinitely renormalizable unimodal maps (with arbitrary combinatorics), in any even degree $d$. We then conclude that orbits of renormalization are asymptotic to…

In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total…

The classical straightening theorem as proved by Douady and Hubbard shows that a polynomial-like sequence is hybrid equivalent to a polynomial. We generalize this result to non-autonomous iteration where one considers composition sequences…

The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…

In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…

Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…

Given a polynomial or a rational map f we associate to it a space of maps. We introduce local coordinates in this space, which are essentially the set of critical values of the map. Then we consider an arbitrary periodic orbit of f with…

Answering a question posed by Adam Epstein, we show that the collection of conjugacy classes of polynomials admitting a parabolic fixed point and at most one infinite critical orbit is a set of bounded height in the relevant moduli space.…

It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…

We construct combinatorial Hubbard trees for all unicritical polynomials, and for all exponential maps, for which the critical (singular) value does not escape. More precisely, out of an external angle, or more generally a kneading…

We compute the motivic nearby cycles of functions obtained by composition with a polynomial which is non-degenerate with respect to its Newton polyhedron. Our result involves new convolution operators and generalized nearby cycles.