We study the relation between the centro-affine geometry of starshaped planar curves and the projective geometry of parametrized maps into RP. We show that projectivization induces a map between differential invariants and a bi-Poisson map between Hamiltonian structures. We also show that a Hamiltonian evolution equation for closed star-shaped planar curves, discovered by Pinkall, has the Schwa...

We consider the regularity of measurable solutions χ to the cohomological equation φ = χ ◦ T − χ, where (T,X, μ) is a dynamical system and φ : X → R is a C valued cocycle in the setting in which T : X → X is a piecewise C Gibbs– Markov map, an affine β-transformation of the unit interval or more generally a piecewise C uniformly expanding map of an interval. We show that under mild assumptions,...

A divergence function defines a Riemannian metric g and dually coupled affine connections ∇ and ∇∗ with respect to it in a manifold M . When M is dually flat, that is flat with respect to ∇ and ∇∗, a canonical divergence is known, which is uniquely determined from (M, g,∇,∇∗). We propose a natural definition of a canonical divergence for a general, not necessarily flat, M by using the geodesic ...

In this paper, we extend work of the first author on a crystal structure on rigged configurations of simply-laced type to all non-exceptional affine types using the technology of virtual rigged configurations and crystals. Under the bijection between rigged configurations and tensor products of Kirillov–Reshetikhin crystals specialized to a single tensor factor, we obtain a new tableaux model f...

We introduce two algebraic completely integrable analogues of the Mumford systems which we call hyperelliptic Prym systems, because every hyperelliptic Prym variety appears as a fiber of their momentum map. As an application we show that the general fiber of the momentum map of the periodic Volterra lattice ȧi = ai(ai−1 − ai+1), i = 1, . . . , n, an+1 = a1, is an affine part of a hyperelliptic ...

Synchronisation arises in dynamical systems that are composed of a number of interconnected subsystems. In the paper synchronization in a particular application a supermarket refrigeration system is studied. The temperature control in supermarket display cases is typically maintained by a number of distributed hysteresis controllers. Synchronization is then manifested by the opening and closing...

We prove that the norm-square of a moment map associated to a linear action of a compact group on an affine variety satisfies a certain gradient inequality. This allows us to bound the gradient flow, even if we do not assume that the moment map is proper. We describe how this inequality can be extended to hyperkähler moment maps in some cases, and use Morse theory with the norm-squares of hyper...

zw Let G be a finite abelian group and M an o-minimal expansion of Rexp = (R, +, ·, <, e) admitting the C∞ cell decomposition. Everything is considered in M. We prove that every definable C∞G manifold is affine. Moreover we prove that if X1, . . . , Xn (resp. Y1, . . . , Yn) are definable C ∞G submanifolds of a definable C∞G manifold X (resp. Y ) in general position, then every definable CG map...

We present an algebraic solution to both direct and featurebased registration of diffusion tensor images under various local deformation models. In the direct case, we show how to linearly recover a local deformation from the partial derivatives of the tensor using the so-called Diffusion Tensor Constancy Constraint, a generalization of the brightness constancy constraint to diffusion tensor da...

On the polytope defined in [FFL11], associated to any rectangle highest weight, we define a structure of an type An-crystal. We show, by using the Stembridge axioms, that this crystal is isomorphic to the one obtained from Kashiwara’s crystal bases theory. Further we define on this polytope a bijective map and show that this map satisfies the properties of a weak promotion operator. This implie...