Gauge theory for finite-dimensional dynamical systems.

  title={Gauge theory for finite-dimensional dynamical systems.},
  author={Pini Gurfil},
  volume={17 2},
Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This concept has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems. We focus on the concept of rescriptive gauge symmetry, which is, in essence, rescaling of an independent variable. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic… 
4 Citations

Figures from this paper

Classical Gauge Principle - From Field Theories to Classical Mechanics
In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the
A Note about Certain Arbitrariness in the Solution of the Homological Equation in Deprit's Method
Deprit’s method has been revisited in order to take advantage of certain arbitrariness arising when the inverse of the Lie operator is applied to obtain the generating function of the Lie transform.
Cointegration of the Daily Electric Power System Load and the Weather
The paper makes a thermal predictive analysis of the electric power system security for a day ahead by cointegrating the daily electric power systen load and the weather and finding the dailyElectric power system thermodynamics and by introducing tests for this thermodynamics.


The Hamiltonian structure of the Maxwell-Vlasov equations
The method of variation of constants and multiple time scales in orbital mechanics.
It is shown that constraints in the method of variation of constants can be generalized in analogy to gauge theories in physics, and that different constraints can offer conceptual advances and methodological benefits to the solution of the underlying problem.
Equations for the orbital elements: Hidden Symmetry
We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain
Numerical simulations of chaotic dynamics in a model of an elastic cable
The finite motions of a suspended elastic cable subjected to a planar harmonic excitation can be studied accurately enough through a single ordinary-differential equation with quadratic and cubic
Gauge freedom in the N-body problem of celestial mechanics
The goal of this paper is to demonstrate how the internal symmetry of the N-body celestial-mechanics problem can be exploited in orbit calculation. We start with summarising research reported in
Partial Lyapunov exponents in tangent space dynamics
The authors have developed a new diagnostic tool for the analysis of the order-to-chaos transition: the partial Lyapunov exponents, defined through the dynamics in the tangent space. They allow the
Pattern evocation and geometric phases in mechanical systems with symmetry
This paper is concerned with the relation between the dynamics of a given Hamiltonian system with a given symmetry group and its reduced dynamics. We illustrate the process of visualization of
Sticky orbits in a kicked-oscillator model
We study a four-fold symmetric kicked-oscillator map with sawtooth kick function. For the values of the kick amplitude λ =2 cos (2π p/q) with rational p / q, the dynamics is known to be
Gauge symmetry of the N-body problem in the Hamilton–Jacobi approach
In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton–Jacobi method: one begins with the two-body Hamilton equations in spherical coordinates,