Related papers: Momentum Map and Action-Angle Variables for Nambu …

The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or…

We studied that arbitrary 2-dimensional maps are Hamilton system if a initial value of map is a "time" variable. In this paper, we generalize this correspondence, and show that an n-dimensional map is a Nambu system in which one of initial…

Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in…

Using the framework of Nambu's generalised mechanics, we obtain a new description of constrained Hamiltonian dynamics, involving the introduction of another degree of freedom in phase space, and the necessity of defining the action integral…

In this thesis we study the classical and quantum momentum maps and the theory of reduction. We focus on the notion of momentum map in Poisson geometry and we discuss the classification of the momentum map in this framework. Furthermore, we…

Due to the emergence of symplectic geometry, the geometric treatment of mechanics underwent a great development during the last century. In this scenario the pressence of symmetries in Hamiltonian systems leads naturally to the existence of…

This paper presents a set-up for momentum map reduction of nonholonomic systems with symmetries, extending previous constructions in [3,25], based on the existence of certain conserved quantities and making essential use of the nonholonomic…

Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is…

Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…

We propose a variant formulation of Hamiltonian systems by the use of variables including redundant degrees of freedom. We show that Hamiltonian systems can be described by extended dynamics whose master equation is the Nambu equation or…

In Hamiltonian mechanics, a (continuous) symmetry leads to conserved quantity, which is a function on (extended) phase space. In Nambu mechanics, a straightforward consequence of symmetry is just a relative integral invariant, a…

This paper presents a reduction procedure for nonholonomic systems admitting suitable types of symmetries and conserved quantities. The full procedure contains two steps. The first (simple) step results in a Chaplygin system, described by…

We develop a reduction scheme \`a la Marsden-Weinstein-Meyer for hybrid Hamiltonian systems. Our method does not require the momentum map to be equivariant, neither to be preserved by the impact map. We illustrate the applicability of our…

We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…

This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of generalized hybrid momentum map and hybrid constants of the motion…

For a differentiable map $(x_1,x_2,..., x_n)\to (X_1,X_2,..., X_n)$ that has an inverse, we show that there exists a Nambu-Hamiltonian flow in which one of the initial value, say $x_n$, of the map plays the role of time variable while the…

Subtraction schemes provide a systematic way to compute fully-differential cross sections beyond the leading order in the strong coupling constant. These methods make singular real-emission corrections integrable in phase space by the…

In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate.…

The classical representation of Hamiltonian systems in terms of action-angle variables are defined for simply connected domains such as an interior of a homoclinic orbit. On this basis methods of (local) perturbations leading, in…

Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…