Related papers: A system of unstable higher Toda brackets
We define inductively unstable n-fold Toda brackets for every n>2 in the category of spaces with base points, and then define stable ones.
We define subscripted unstable higher Toda brackets and study their elementary properties. This paper is the continuation of our previous paper in which we defined the non-subscripted unstable higher Toda brackets.
We construct Toda brackets in unstable motivic homotopy theory and prove some fundamental properties of them. Furthermore we construct some examples of motivic Toda brackets.
We describe two ways to define higher order Toda brackets in a pointed simplicial model category $\mathcal{D}$: one is a recursive definition using model categorical constructions, and the second uses the associated simplicial enrichment.…
We define two new unstable n-fold Toda brackets for every composable sequence (f_n, ... ,f_1) of pointed maps f_i : X_i \to X_{i+1} between well-pointed spaces with n > 2. The brackets agree with the classical Toda bracket when n = 3, and…
We provide a general definition of Toda brackets in a pointed model categories, show how they serve as obstructions to rectification, and explain their relation to the classical stable operations.
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 provide a uniform definition of higher order Toda brackets in a general setting, covering the known cases of long Toda brackets for topological spaces and chain complexes and Massey products for differential graded algebras, among…
In this paper we consider the unstable chaotic attractor of the Toda potential and stabilize it by a control in integral form. In order to obtain stability results, we propose a special technique which is based on the idea of reduction of…
New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…
In this manuscript, a modified $R_I$ type recurrence relation is considered whose recurrence coefficients are perturbed by addition or multiplication of a constant. The perturbed system of recurrence coefficients is represented by Toda…
We construct more non-trivial examples for Toda brackets in unstable motivic homotopy theory via the first and second motivic Hopf maps.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure.
A simple procedure to enumerate all Toda systems associated with complex classical Lie groups is given.
This article addresses the question of involutiveness and discusses the initial value problem for a class of overdetermined systems of partial differential equations which arise in the theory of integrable systems and are defined by…
In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carath\'{e}odory dimension characteristic, motivated by the work of Bowen and Pesin etc. We…
The superintegrability of the non-periodic Toda lattice is explained in the framework of systems written in action-angles coordinates. Moreover, a simpler form of the first integrals is given.
The purpose of this material is to review the Adler Kostant Symes scheme as a theory which can be developped succesfully in different contexts. It was useful to describe some mechanical systems, the so called generalized Toda, and now it…
In the present paper we obtain some integrable generalisations of the Toda system generated by flat connection forms taking values in higher ${\bf Z}$--grading subspaces of a simple Lie algebra, and construct their general solutions. One…