Related papers: The Adler Kostant Symes scheme in physics
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
This paper describes the notion of \sigma -symmetry, which extends the one of \lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider…
Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
We expose some selected topics concerning the instability of the action variables in a priori unstable Hamiltonian systems, and outline a new strategy that may allow to apply these methods to a priori stable systems.
In this paper, we define an invariant, which we believe should be the substitute for total K-theory in the case when there is one distinguished ideal. Moreover, some diagrams relating the new groups to the ordinary K-groups with…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
We present a notion of symmetry for 1+1-dimensional integrable systems which is consistent with their group theoretic description and reproduces in special cases the known Baecklund transformation for the generalized Korteweg-deVries…
The realization of novel scenario involving transitions between different types of chaotic attractors is investigated for the Rossler system. Characteristic features indicative of the presence of generalized intermittency scenario in this…
In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers…
We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schr\"odinger algebra, these equations…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
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…
For a one-dimensional motion, a constant of motion for non autonomous an linear system (position and velocity) is given from the constant of motion associated to its autonomous system. This approach is used in the study of the harmonic…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
I present a discussion of the hierarchy of Toda flows that gives center stage to the associated cocycles and the maps they induce on the $m$ functions. In the second part, these ideas are then applied to canonical systems; an important…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…