A bi–Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in a case it connects an integrable Hénon–Heiles system and the Garnier system. Moreover a new integrability scheme for Hamiltonian systems is proposed, holding in the standard phase space. Date: Dipartimento di Scienze...

We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural isomorphism between a moduli space of spectral data and a moduli space of differential data, each equipped with an infinite collection of commuting flows. The spect...

‎in this work we introduce and study discrete time periodically correlated stable‎ ‎processes and multivariate stationary stable processes related to periodic and cyclic‎ ‎flows‎. ‎our study involves producing a spectral representation and a‎ ‎spectral identification for such processes‎. ‎we show that the third‎ ‎component of a periodically correlated stable process has a component related to a...

We study flows on the space of topological Landau-Ginzburg theories coupled to topological gravity. We argue that flows corresponding to gravitational descendants change the target space from a complex plane to a punctured complex plane and lead to the motion of punctures.It is shown that the evolution of the topolog-ical theory due to these flows is given by dispersionless limit of KP hierarch...

We review recent developments in the theory of renormalisation group flows in minimal models with boundaries. Among these, we discuss in particular the perturbative calculations of Recknagel et al, not only as a tool to predict the IR endpoints of certain flows, but also as a motivation for considering the particular limiting case of c=1. By treating this limit, we are able to investigate a wid...