Related papers: The Adler Kostant Symes scheme in physics
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with…
Integral discriminants provide a simple and fundamental model for non-Gaussian integrals, associated with homogeneous polynomials of degree r in n variables. We argue that, in this context, the study of correlators is equally if not more…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter dependent family - via the Poincar\'e Normal Form approach. We discuss this at first formally, and…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will…
In the present work a Cartan mechanics version for Routh reduction is considered, as an intermediate step toward Routh reduction in field theory. Motivation for this generalization comes from an scheme for integrable systems [12], used for…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
A nonholonomic system is a mechanical system with velocity constraints not originating from position constraints; rolling without slipping is the typical example. A nonholonomic integrator is a numerical method specifically designed for…
The affine Toda field theory is studied as a 2+1-dimensional system. The third dimension appears as the discrete space dimension, corresponding to the simple roots in the $A_N$ affine root system, enumerated according to the cyclic order on…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
A cross between two well-known integrable multi-particle dynamics, an affine Toda molecule and a Sutherland system, is introduced for any affine root system. Though it is not completely integrable but partially integrable, or quasi exactly…
In this paper we present a-posteriori KAM results for existence of $d$-dimensional isotropic invariant tori for $n$-DOF Hamiltonian systems with additional $n-d$ independent first integrals in involution. We carry out a covariant…
The question of the integrability of the mixmaster model of the Universe, presented as a dynamical system with finite degrees of freedom, is investigated in present paper. As far as the model belongs to the class of pseudo-Euclidean…
The Noether-Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we…
We investigate the integrals of motion of general conformal mechanical systems with and without confining harmonic potential as well as of the related angular subsystems, by employing the SL(2,R) algebra and its representations. In…