Related papers: There is only one KAM curve
The classical Cartan's structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of…
We derive a uniqueness result for non-Cartesian composition of systems in a large class of process theories, with important implications for quantum theory and linguistics. Specifically, we consider theories of wavefunctions valued in…
A uniqueness theorem is established for autonomous systems of ODEs, $\dot{x}=f(x)$, where $f$ is a Sobolev vector field with additional geometric structure, such as delta-monoticity or reduced quasiconformality. Specifically, through every…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
We show that isotopy classes of simple closed curves in any oriented surface admit a quandle structure with operations induced by Dehn twists, the Dehn quandle of the surface. We further show that the monodromy of a Lefschetz fibration can…
This paper provides an extensive study of the homotopy theory of types of algebras with units, like unital associative algebras or unital commutative algebras for instance. To this purpose, we endow the Koszul dual category of curved…
We consider Gevrey perturbations $H$ of a completely integrable Gevrey Hamiltonian $H_0$. Given a Cantor set $\Omega_\kappa$ defined by a Diophantine condition, we find a family of KAM invariant tori of $H$ with frequencies $\omega\in…
We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincare duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincare duality in the same…
In this note we present a new KAM result which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is…
This paper introduces a general technique for inter-mapping the complex spatial frequency (or propagation constant) $\gamma=\alpha+j\beta$ and the temporal frequency $\omega = \omega_\text{r}+j\omega_\text{i}$ of an arbitrary…
In this paper we study a natural extension of Kontsevich's characteristic class construction for A-infinity and L-infinity algebras to the case of curved algebras. These define homology classes on a variant of his graph homology which…
We consider an area-minimizing integral current $T$ of codimension higher than 1 ins a smooth Riemannian manifold $\Sigma$. We prove that $T$ has a unique tangent cone, which is a superposition of planes, at $\mathcal{H}^{m-2}$-a.e. point…
We discuss the invariant classification of vacuum Kundt waves using the Cartan-Karlhede algorithm, and the upper bound on the number of iterations of the Karlhede algorithm to classify the vacuum Kundt waves. By choosing a particular…
A compact real analytic Riemannian manifold M admits a canonical complexification with plurisubharmonic exhaustion function satisfying the homogeneous complex Monge-Ampere equation, called a Grauert tube. From the point of view of complex…
Given a germ of a smooth plane curve $(\{f(x,y)=0\},0)\subset (\mathbb K^2,0), \mathbb K=\mathbb R, \mathbb C$, with an isolated singularity, we define two invariants $I_f$ and $V_f\in \mathbb N\cup\{\infty\}$ which count the number of…
We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian perturbations of the dispersive Degasperis-Procesi equation on the circle. The overall strategy in KAM theory for quasi-linear PDEs is based on Nash-Moser…
The core of quantum tomography is the possibility of writing a generally unbounded complex operator in form of an expansion over operators that are generally nonlinear functions of a generally continuous set of spectral densities--the…
In this note we develop some properties of those algebras (called here locally simple) which can be generated by a single element after, if need be, a faithfully flat extension. For finite algebras, this is shown to be in fact a property of…
In the following we are interested in the spectral gaps of discrete quasiperiodic Schr\"odinger operators when the frequency is Diophantine, the potential is analytic, and in the subcritical regime. The gap-labelling theorem asserts in this…
We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalised species over locally bounded quivers. We prove that analogues of the kernel and cokernel functor…