Related papers: Flows of birational quadratic transformations in t…

Bertini classified the birational involutions of the complex projective plane, but his geometric approach does not allow to explicit these maps easily. In this article, we present an effective approach to this problem by associating to each…

We propose a geometric construction of three-dimensional birational maps that preserve two pencils of quadrics. The maps act as compositions of involutions, which, in turn, act along the straight line generators of the quadrics of the first…

Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric…

This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.

We use confocal microscopy to directly visualize the spatial fluctuations in fluid flow through a three-dimensional porous medium. We find that the velocity magnitudes and the velocity components both along and transverse to the imposed…

We classify endomorphisms of the plane that preserve a pencil of curves.

This is a continuation of the authors' earlier work on deformations of cuspidal edges. We give a representation formula for swallowtails in the Euclidean 3-space. Using this, we investigate map germs of generic swallowtails in 3-dimensional…

We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional…

Since the end of the XIXth century, we know that each birational map of the complex projective plane is the product of a finite number of quadratic birational maps of the projective plane; this motivates our work which essentially deals…

We show that every morphism from a degree 5 hypersurface in 4-dimensional projective space to a nonsingular degree 3 hypersurface in 4-dimensional projective space is necessarily constant. In the process, we also classify morphisms from the…

Many dense granular systems are non-monodisperse, consisting of particles of different sizes, and will segregate based on size during flow. This phenomenon is an important aspect of many industrial and geophysical processes, necessitating…

Kahan discretization is applicable to any quadratic vector field and produces a birational map which approximates the shift along the phase flow. For a planar quadratic Hamiltonian vector field with a linear Poisson tensor and with a…

This paper aims to study canonical pencils of higher dimensional projective varieties. It seems that the geometric genus of the general fibre for the derived fibration from the canonical pencil for a 3-fold of general type does not have an…

There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…

Manin transformations are maps of the plane that preserve a pencil of cubic curves. They are the composition of two involutions. Each involution is constructed in terms of an involution point that is required to be one of the base points of…

We use the bailout embeddings of three-dimensional volume-preserving maps to study qualitatively the dy- namics of small spherical neutrally buoyant impurities suspended in a time-periodic incompressible fluid flow. The accumulation of…

In this paper we prove the following topological classification result for flows on real projective space induced by linear flows on Euclidean space: Two flows on the projective space P(V) of a finite-dimensional real vector space V,…

We consider the general problem of mixing of Gaussian solute plumes arising across a range of different flows ranging from two-dimensional (2D) to three-dimensional (3D), steady to unsteady, regular to chaotic, Stokes to turbulent. We…

This article studies germs of holomorphic vector fields at the origin of C3 that are tangent to holomorphic foliations of codimension one. Two situations are considered. First, we assume hypotheses on the reduction of singularities of the…

A birational map from a projective space onto a not too much singular projective variety with a single irreducible non-singular base locus scheme (special birational transformation) is a rare enough phenomenon to allow meaningful and…