Related papers: Toda maps, cocycles, and canonical systems
In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. In this paper we construct other examples of integrable dynamics of Toda-type on the square lattice, as well as on the triangular lattice,…
In the present paper we obtain some integrable generalisations of the continuous Toda system generated by a flat connection form taking values in higher grading subspaces of the algebra of the area--preserving diffeomorphism of the torus…
A new integrable lattice system is introduced, and its integrable discretizations are obtained. A B\"acklund transformation between this new system and the Toda lattice, as well as between their discretizations, is established.
We study linear relations among correlation functions on a lattice obtained from integration-by-parts identities. We use the framework of twisted cocycles and determine for a scalar theory a basis of correlation functions, in which all…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
Passing from a microscopic discrete lattice system with many degrees of freedom to a mesoscopic continuum system described by a few coarse-grained equations is challenging. The common folklore is to take the thermodynamic limit so that the…
Variation of coupling constants of integrable system can be considered as canonical transformation or, infinitesimally, a Hamiltonian flow in the space of such systems. Any function $T(\vec p, \vec q)$ generates a one-parametric family of…
Applying recent ideas of Carlet, Dubrovin and Zhang (to appear), who, following a suggestion of Eguchi and Yang (hep-th/9407134), study the logarithm of the Lax operator of the Toda lattice, we show that the equivariant Toda lattice…
We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure…
We give a detailed proof that locally Noetherian moduli stacks of sections carry canonical obstruction theories. As part of the argument we construct a dualizing sheaf and trace map, in the lisse-etale topology, for families of tame twisted…
This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…
In this paper we define a family of systems which have similarities with the Toda lattice. We construct two Lax pair representations and the associate Poisson structures for these systems. These systems lie between the classical Toda…
This article is meant as a mathematical appendix or comment on [BT]. We first consider the notion of transcritical bifurcations of fixed points of general area-preserving maps, and then adress some questions related to [BT] on bifurcation…
Generalizing a construction of A. Weil, we introduce a topological invariant for flows on compact, connected, finite dimensional, abelian, topological groups. We calculate this invariant for some examples and compare the invariant with…
We discuss the generic definition of the $\tau$ function for the arbitrary Hamiltonian system. The different approaches concerning the deformations of the curves and surfaces are compared. It is shown that the Baker-Akhiezer function for…
The $q$-Toda equation is derived from replacing ordinary derivatives with $q$-derivatives in the famous Toda equation. In this paper, we associate an extension of the $q$-Toda equation with matrix eigenvalue problems, and then show…
A two cocycle is associated to any action of a Lie group on a symplectic manifold. This allows to enlarge the concept of anomaly in classical dynamical systems considered by F. Toppan [in J. Nonlinear Math. Phys. 8, no.3 (2001) 518-533] so…
We discuss a relation between bicomplexes and integrable models, and consider corresponding noncommutative (Moyal) deformations. As an example, a noncommutative version of a Toda field theory is presented.
We start the study of the family of birational maps $(f_{\alpha,\beta})$ of $\mathbb{P}^2_\mathbb{C}$ in \cite{Deserti}. For generic $\alpha$ and $\beta$ of modulus 1 the centraliser of $f_{\alpha,\beta}$ is trivial, the topological entropy…
We study the equivariant cobordism theory of schemes for action of linear algebraic groups. We compare the equivariant cobordism theory for the action of a linear algebraic groups with similar groups for the action of tori and deduce some…