相关论文: Soliton Dynamics in Computational Anatomy

Snapshot matrices of hyperbolic equations have a slow singular value decay, resulting in inefficient reduced-order models. We develop on the idea of inducing a faster singular value decay by computing snapshots on a transformed spatial…

We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of kappa-deformations of the Poincare algebra with associated momenta living on (a…

The three-body general problem is formulated as a problem of geodesic trajectories flows on the Riemannian manifold. It is proved that a curved space with local coordinate system allows to detect new hidden symmetries of the internal motion…

To a system of second order ordinary differential equations (SODE) one can assign a canonical nonlinear connection that describes the geometry of the system. In this work we develop a geometric setting that allows us to assign a canonical…

We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one…

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…

For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the…

In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the Euler-Poincar\'e theory. In the metamorphosis of images, the Lie group of diffeomorphisms deforms…

We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…

Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…

We develop a monadic framework formalising an operational notion of dynamics, seen as the setting and evolution of initial value problems, in general physical theories. We identify in the Eilenberg-Moore category the natural environment for…

We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality…

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the…

The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…

The Hamiltonian action of a Lie group on a symplectic manifold induces a momentum map generalizing Noether's conserved quantity occurring in the case of a symmetry group. Then, when a Hamiltonian function can be written in terms of this…

We give a review of the systematic construction of hierarchies of soliton flows and integrable elliptic equations associated to a complex semi-simple Lie algebra and finite order automorphisms. For example, the non-linear Schr\"odinger…

This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…

We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the…

In computational anatomy, the statistical analysis of temporal deformations and inter-subject variability relies on shape registration. However, the numerical integration and optimization required in diffeomorphic registration often lead to…

A connection between differential geometry and soliton equations is discussed