Related papers: A computation of invariants of a rational self-map
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We study Gromov-Witten invariants on the blow-up of P^n at a point, which is probably the simplest example of a variety whose moduli spaces of stable maps do not have the expected dimension. It is shown that many of these invariants can be…
We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals. The bounds are uniform in the curve and involve the rank of the corresponding Jacobian. The method used in the proof is a…
This note will discuss the dynamics of iterated cubic maps from the real or complex line to itself, and will describe the geography of the parameter space for such maps. It is a rough survey with few precise statements or proofs, and…
This will is an expository description of quadratic rational maps. Sections 2 through 6 are concerned with the geometry and topology of such maps. Sections 7--10 survey of some topics from the dynamics of quadratic rational maps. There are…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
We consider the locus of irreducible nonsingular rational curves of degree d Pn, n>2, meeting a generic collection of linear subspaces. When this locus is 0 (resp 1)- dimensional, we compute (recursively) its degree (resp. geometric genus).…
In this paper we adapt some techniques developed for K3 surfaces, to study the geometry of a family of projective varieties in $\Pl_K^2 \times \Pl_K^2 \times \Pl_K^2$ defined as the intersection of a form of degree $(2,2,2)$ and a form of…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We discuss some examples of geometrically meaningful rational self-maps of moduli space of curves of low genus and homogeneous forms.
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
We study the moduli spaces of rational curves on prime Fano threefolds of index 1. For general threefolds of most genera we compute the dimension and the number of irreducible components of these moduli spaces. Our results confirm Geometric…
We use the version of the Lyapunov--Perron method operating on individual solutions to investigate the existence of invariant manifolds for non-autonomous dynamical systems, focusing in particular on inertial and stable manifolds. We…
We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{some} quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to…
A systematic study of non-trivial cubic extensions of the four-dimensional Poincar\'e algebra is undertaken. Explicit examples are given with various techniques (Young tableau, characters etc).