Related papers: Dynamical systems with a parallel tensor

We prove that the Kontsevich tetrahedral flow $\dot{\mathcal{P}} = \mathcal{Q}_{a:b} (\mathcal{P})$, the right-hand side of which is a linear combination of two differential monomials of degree four in a bi-vector $\mathcal{P}$ on an affine…

A tensor ${\mathcal A}$ of order $m$ and dimension $n$ is called a ${\rm Q}$-tensor if the tensor complementarity problem has a solution for all ${\bf q} \in {\mathbb R}^{n}$. This means that for every vector ${\bf q}$, there exists a…

We prove a theorem on structural stability of smooth attractor-repellor endomorphisms of compact manifolds, with singularities. By attractor-repellor, we mean that the non-wandering set of the dynamics $f$ is the disjoint union of a…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…

Let X be a compact nonsingular real algebraic variety. We prove that if a continuous map from X into the unit p-sphere is homotopic to a continuous rational map, then, under certain assumptions, it can be approximated in the compact-open…

We prove that if a certain entry in the map of the Hadamard-Perron theorem is $T$-periodic in one of the variables, then the stable manifold guaranteed by the Hadamard-Perron theorem is a graph of a $T$-periodic function. As an application,…

We present a natural extension of the notion of nondegenerate rational maps (quadrirational maps) to arbitrary dimensions. We refer to these maps as $2^n-$rational maps. In this note we construct a rich family of $2^n-$rational maps. These…

Dynamical systems often admit geometric properties that must be taken into account when studying their behaviour. We show that many such properties can be encoded by means of quiver representations. These properties include classical…

We study new classes of linear preservers between C$^*$-algebras and JB$^*$-triples. Let $E$ and $F$ be JB$^*$-triples with $\partial_{e} (E_1)$. We prove that every linear map $T:E\to F$ strongly preserving Brown-Pedersen quasi-invertible…

In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.

We introduce a subclass of recursive subhomogeneous algebras, in which each of the pullback maps is diagonal in a suitable sense. We define the notion of a diagonal map between two such algebras and show that every simple inductive limit of…

We show in many cases that there exist rational scrolls which are balanced, i.e. they contain the expected number of general linear spaces as rulings. For example, there exist balanced scrolls of degree $mk+1$ and fibre dimension $k$ in…

Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections P_a determined by the different involutions #_a induced by positive invertible elements a…

We consider surjective endomorphisms f of degree > 1 on projective manifolds X of Picard number one and their f^{-1}-stable hypersurfaces V, and show that V is rationally chain connected. Also given is an optimal upper bound for the number…

We consider diffeomorphisms $f$ with heteroclinic cycles associated to saddles $P$ and $Q$ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to $f$ with a robust cycle associated to…

For a coarse space $(X, \mathcal{E})$, $X^\sharp$ denotes the set of all unbounded ultrafilters on $X$ endowed with the parallelity relation: $p||q$ if there exists $E \in \mathcal{E} $ such that $ E[P]\in q $ for each $P\in p$. If $(X,…

In a triangulated symmetric monoidal closed category, there are natural dualities induced by the internal Hom. Given a monoidal functor f^* between two such catgories and adjoint couples (f^*,f_*) and (f_*,f^!), we prove the necessary…

If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent --i.e. equivalent via a classical diffeomorphism-- or they are both ruled; for systems of different…

The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…

We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…