Related papers: A concrete co-existential map that is not confluen…
In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic…
In this paper we give an example of a closed, strongly one-sided dense set which is not of uniform density type. We also show that there is a set of uniform density type which is not of strong uniform density type.
New global periodic orbit collision/separatrix reconnection scenarios in the standard nontwist map in different regions of parameter space are described in detail, including exact methods for determining reconnection thresholds that are…
We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities.
In this paper we study noncommutative plane curves, i.e. non-commutative k-algebras for which the 1-dimensional simple modules form a plane curve. We study extensions of simple modules and we try to enlighten the completion problem, i.e.…
We show that every cross ratio preserving homeomorphism between boundaries of Hadamard manifolds extends to a continuous map, called circumcenter extension, provided that the manifolds satisfy certain visibility conditions. We show that…
We introduce two new algebraic invariants, the (co)homological distances between continuous maps, which provide computable lower bounds for the homotopic distance and strictly refine the classical cup-length estimates. We then define the…
A reinterpretation of noncommutativity as a mapping of paths is proposed at the level of quantum mechanics.
Our aim is to prove the integration formula on the noncommutative (Moyal) plane in terms of singular traces {\it a la} Connes.
The aim of this note is to characterize trees, endowed with coarse wedge topology, that have a retractional skeleton. We use this characterization to provide new examples of non-commutative Valdivia compact spaces that are not Valdivia.
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings…
We give an example of a non-trivial linear operad that only admits trivial coalgebras and give sufficient conditions ensuring that the cofree coalgebra functor be faithful.
We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to…
We prove that the non-commutative perspective of an operator convex function is the unique extension of the corresponding commutative perspective that preserves homogeneity and convexity.
We show that a $C^1$-generic expanding map of the circle has no absolutely continuous invariant $\sigma$-finite measure.
We consider a generalised non-commutative space-time in which non-commutativity is extended to all phase space variables. If strong enough, non-commutativity can affect stability of the system. We perform stability analysis on a couple of…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, and its extensions for the interaction between an incompressible, viscous fluid and a thin, elastic…
We study phase separation between coexisting active and passive fluids in three-dimensions, using numerical simulation and experiments. Chaotic flows of the active phase drive giant interfacial deformations, causing the co-existing phases…
We construct a $C^1$ symplectic twist map f of the annulus that has an essential invariant curve C such that: --C is not differentiable; -- the dynamic of f restricted to C is conjugated to the one of a Denjoy counter-example.